tag:blogger.com,1999:blog-81737329255277537372024-03-13T14:13:01.144-07:00GMAT / MAT / KMAT / Pg CET Mba Entrance examsAdministratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.comBlogger22125tag:blogger.com,1999:blog-8173732925527753737.post-9708019980106642942011-07-05T06:01:00.000-07:002011-07-05T06:01:06.085-07:00Application Form for Karnataka Post Graduate Common Entrance Test 20111. The candidates have to procure the PGCET 2011 MCA / MBA brochure cum application form by Speed Post only by sending a self addressed cloth-lined envelope of size 25 cm X 30 cm along with the prescribed fee of 600/- in the form of demand draft drawn in favour of “The Executive Director, Karnataka Examinations Authority”, payable at Bangalore. ( 300/- in case of Karnataka SC, ST and Category-I Candidates )<br />
<br />
2. If a candidate likes to apply for more than one course ( eg. for both MBA and MCA ) then he she is required to apply separately by sending two different covers with two different requisite demand drafts each, as the case may be.<br />
<br />
3. The contents on the self addressed envelope should be in English or Kannada language only. The cover in which the demand draft and self addressed envelope are sent should be boldly super scribed with the words “Request for PGCET 2011 Brochure for course” ( MBA / MCA / M.E. / M. Tech. / M. Arch / MBA ( Infrastructure Management etc. ) and should be sent to the following address By Speed Post only.<br />
<br />
The Executive Director,<br />
Karnataka Examinations Authority,<br />
18th Cross, Sampige Road,<br />
Malleshwaram,<br />
Bangalore – 560 012. <br />
4. KEA will not take responsibility for the envelopes sent through courier or given in person or through any other private arrangement and also for incomplete and insufficient address on the envelope.<br />
<br />
5. The Last Date for PGCET Entrance Exam 2011 Application submission of Demand Drafts to KEA to obtain brochure cum application form is 25-06-2011 5.00 P.M.<br />
<br />
PGCET 2011 Karnataka Important Dates :<br />
<br />
1) The PGCET Karnataka brochure cum application form will be sent by speed post to the home address of the candidates furnished on the self addressed cloth lined cover on or after 02-07-2011.<br />
<br />
2) Last date for submission of filled PGCET Application form by Speed Post to KEA is 15-07-2011 5.00 P.M.<br />
<br />
3) Karnataka Examination will be conducted only in the state of Karnataka at various places as specified in the PGCET 2011 Brochure.Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-5142435136578799032011-05-01T01:06:00.001-07:002011-05-01T01:06:50.079-07:00Prepositions<b><b>What are prepositions?<br />
<br />
Prepositions are words that specify place, direction, and time. There are three types of prepositions.<br />
<br />
Time Prepositions - Time prepositions define time. Time prepositions - In - At - On For - During - While <br />
<br />
Place Propositions - Place prepositions clarify the place someone or somebody. Place Prepositions - In - On -At<br />
<br />
Direction Prepositions - Direction prepositions are used to clarify the direction of someone or something. Examples: under, over, right, left etc. <br />
</b></b>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-26085325202509454112011-04-17T11:24:00.000-07:002011-04-23T22:25:23.074-07:00Problems on Clocks<div dir="ltr" style="text-align: left;" trbidi="on"><marquee> <b> <font color="223344">Clocks </font></b> </marquee><br />
<b><span style="font-size: large;">Problems on Clocks</span></b><br />
<b><br />
</b><span style="font-size: large;">General Concepts </span><br />
<span style="font-size: large;">The face or dail of a watch is a circle whose circumference is divided into 60 equal parts , called minute spaces. </span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">A clock has two hands , the smaller one is called the hour hand or short hand while the larger hand is called the minute hand or long hand. </span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">In 60 minutes , the minute hand gains 55 minutes on the hour hand. </span><br />
<span style="font-size: large;">In every hour , both the hands coincide once. </span><br />
<span style="font-size: large;">The hands are in the same straight line when they are coincident or opposite to each other </span><br />
<span style="font-size: large;">When the two hands are at right angles, they are 15 minute spaces apart. </span><br />
<span style="font-size: large;">When the hands are in opposite directions, they are 30 minute spaces apart. </span><br />
<span style="font-size: large;">Too Fast and Too Slow :If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">On the other hand , if it indicates 7.45, when the correct time is 8, it is said to be too slow.</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Solved Problems</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">1. Find the angle between the minute hand and hour hand of a clock when the time is 7.20</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Sol : Angle traced by hour hand in 12 hours = 360 Degrees</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Angle traced by it in 7 hrs 20 min i.e 22/3 hrs = (360/12) x (22/3)= 2200</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Angle traced by minute hand in 60 min = 3600</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Angle traced by it in 20 minutes = (360/60) x 20 = 1200</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Required angle = (2200 - 1200) = 1000</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">2. At what time between 2 and 3 o' clock will the hands of a clock together ?</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Sol : At o' clock, the hour hand is at 2 and minute hand at 12, i.e they are 10 minute spaces apart.</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">To be together , the minute hand must gain 10 minutes over the hour hand.</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Now, 55 minutes are gaines by it in 60 minutes</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">10 minutes will be gained in {(60/55) x 10} min =10 10/11 min</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">The hands will coincide at 10 10/11 min past 2</span><span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">3. At what time between 4 and 5 o' clock will the hands of a clock be at right angle ?</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Sol : At 4 o' clock, the minute hand will be 20 min spaces behind the hour hand.</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Now , when the two hands are at right angles , they are 15 min. spaces apart.</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">So, they are at right angles in following two cases</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Case I : When minute hand is 15 minute spaces behind the hour hand</span><span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">In this case min hand will have to gain (20 -15) = 5 minute spaces</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">55 min. spaces will be gained by it in (60 x 5)/55 min = 5 5/11 min</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">They are at right angles at 5 5/1 min past 4</span><br />
<span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">Case II : When the minute hand is 15 minute spaces ahead of the hour hand</span><span style="font-size: large;"><br />
</span><br />
<span style="font-size: large;">They are at right angles at 38 2/11 min past 4</span><br />
<span style="font-size: large;"><br />
</span></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-87494020741860333802011-04-17T09:10:00.001-07:002011-04-17T11:28:05.452-07:00Pipes and Cisterns<div dir="ltr" style="text-align: left;" trbidi="on"><b>Important Facts: <br />
<br />
1.INLET:A pipe connected with a tank or cistern or a reservoir,<br />
that fills it, it is known as Inlet.<br />
<br />
OUTLET:A pipe connected with a tank or a cistern or a reservoir,<br />
emptying it, is known as Outlet.<br />
<br />
2. i) If a pipe can fill a tank in x hours, then :<br />
part filled in 1 hour=1/x.<br />
<br />
ii)If a pipe can empty a tank in y hours, then :<br />
part emptied in 1 hour=1/y.<br />
<br />
iii)If a pipe can fill a tank in x hours and another pipe can<br />
empty the full tank in y hours( where y>x), then on<br />
opening both the pipes, the net part filled in<br />
1 hour=(1/x -1/y).<br />
<br />
iv)If a pipe can fill a tank in x hours and another pipe can<br />
empty the full tank in y hours( where x>y), then on opening<br />
both the pipes, the net part filled in 1 hour=(1/y -1/x).<br />
<br />
v) If two pipes A and B can fill a tank in x hours and y hours<br />
respectively. If both the pipes are opened simultaneously, part<br />
filled by A+B in 1 hour= 1/x +1/y.<br />
<br />
Simple Problems<br />
<br />
1)Two pipes A& B can fill a tank in 36 hours and 45 hours respectively.<br />
If both the pipes are opened simultaneously, how much time will be<br />
taken to fill the tank?<br />
<br />
Sol: Part filled by A in 1 hour=1/36<br />
Part filled by B in 1 hour= 1/45;<br />
Part filled by (A+B)’s in 1 hour=1/36 +1/45= 9/180 =1/20<br />
Hence, both the pipes together will fill the tank in 20 hours.<br />
<br />
2)Two pipes can fill a tank in 10 hours & 12 hours respectively. While<br />
3rd pipe empties the full tank n 20 hours. If all the three pipes<br />
operate simultaneously,in how much time will the tank be filled?<br />
<br />
Sol: Net part filled in 1 hour=1/10 +1/12 -1/20<br />
=8/60=2/15<br />
The tank be filled in 15/2hours= 7 hrs 30 min<br />
<br />
3)A cistern can be filled by a tap in 4 hours while it can be emptied<br />
by another tap in 9 hours. If both the taps are opened simultaneously,<br />
then after how much time will the cistern get filled?<br />
<br />
Sol: Net part filled in 1 hour= 1/4 -1/9= 5/36<br />
Therefore the cistern will be filled in 36/5 hours or 7.2 hours.<br />
<br />
4)If two pipes function simultaneously, the reservoir will be filled in<br />
12 days.One pipe fills the reservoir 10 hours faster than the other.<br />
How many hours does it take the second pipe to fill the reservoir.<br />
<br />
Sol: Let the reservoir be filled by the 1st pipe in x hours.<br />
The second pipe will fill it in (x+10) hours<br />
1/x + (1/(x+10))= 1/12<br />
=> (2x+10)/((x)*(x+10))= 1/12<br />
=> x=20<br />
So, the second pipe will take 30 hours to fill the reservoir.<br />
<br />
5)A cistern has two taps which fill it in 12 min and 15 min respectively.<br />
There is also a waste pipe in the cistern. When all the three are opened,<br />
the empty cistern is full in 20 min. How long will the waste pipe take to<br />
empty the full cistern?<br />
<br />
Sol: Work done by a waste pipe in 1 min<br />
=1/20 -(1/12+1/15)= -1/10 (-ve means emptying)<br />
<br />
6)A tap can fill a tank in 6 hours. After half the tank is filled, three<br />
more similar taps are opened. What is the total time taken to fill the<br />
tank completely?<br />
<br />
Sol: Time taken by one tap to fill the half of the tank =3 hours<br />
Part filled by the four taps in 1 hour=4/6=2/3<br />
Remaining part=1 -1/2=1/2<br />
Therefore, 2/3:1/2::1:x<br />
or x=(1/2)*1*(3/2)=3/4 hours.<br />
i.e 45 min<br />
So, total time taken= 3hrs 45min.<br />
<br />
7)A water tank is two-fifth full. Pipe A can fill a tank in 10 min. And B<br />
can empty it in 6 min. If both pipes are open, how long will it take to<br />
empty or fill the tank completely ?<br />
<br />
Sol: Clearly, pipe B is faster than A and So, the tank will be emptied.<br />
Part to be emptied=2/5.<br />
Part emptied by (A+B) in 1 min= 1/6 -1/10=1/15<br />
Therefore, 1/15:2/5::1:x or x=((2/5)*1*15)=6 min.<br />
So, the tank be emptied in 6 min.<br />
<br />
8)Bucket P has thrice the capacity as Bucket Q. It takes 60 turns for<br />
Bucket P to fill the empty drum. How many turns it will take for both the<br />
buckets P&Q, having each turn together to fill the empty drum?<br />
<br />
Sol: Let the capacity of P be x lit.<br />
Then capacity of Q=x/3 lit<br />
Capacity of the drum=60x lit<br />
Required number of turns= 60x/(x+(x/3))= 60x*3/4x=45<br />
<br />
Complex Problems<br />
<br />
1)Two pipes can fill a cistern in 14 hours and 16 hours respectively. The<br />
pipes are opened simultaneously and it is found that due to leakage in the<br />
bottom it took 32min more to fill the cistern. When the cistern is full,<br />
in what time will the leak empty it?<br />
<br />
Sol: Work done by the two pipes in 1 hour= 1/14+1/16=15/112<br />
Time taken by these two pipes to fill the tank=112/15 hrs.<br />
Due to leakage, time taken = 7 hrs 28 min+ 32 min= 8 hours<br />
Therefore, work done by (two pipes + leak) in 1 hr= 1/8<br />
work done by leak n 1 hour=15/112 -1/8=1/112<br />
Leak will empty full cistern n 112 hours.<br />
<br />
2)Two pipes A&B can fill a tank in 30 min. First, A&B are opened. After<br />
7 min, C also opened. In how much time, the tank s full.<br />
<br />
Sol: Part filled n 7 min = 7*(1/36+1/45)=7/20<br />
Remaining part= 1-7/20=13/20<br />
Net part filled in 1 min when A,B and C are opened=1/36 +1/45- 1/30=1/60<br />
Now, 1/60 part is filled in 1 min.<br />
13/20 part is filled n (60*13/20)=39 min<br />
Total time taken to fill the tank=39+7=46 min <br />
<br />
3)Two pipes A&B can fill a tank in 24 min and 32 min respectively. If<br />
both the pipes are opened simultaneously, after how much time B should<br />
be closed so that the tank is full in 18 min. <br />
<br />
Sol: Let B be closed after x min, then part filled by (A+B) in x min+<br />
part filled by A in (18-x) min=1<br />
x(1/24+1/32) +(18-x)1/24 =1<br />
=> x=8<br />
Hence B must be closed after 8 min.<br />
<br />
4)Two pipes A& B together can fill a cistern in 4 hours. Had they been<br />
opened separately, then B would have taken 6 hours more than A to fill<br />
the cistern. How much time will be taken by A to fill the cistern<br />
separately?<br />
<br />
Sol: Let the cistern be filled by pipe A alone in x hours.<br />
Pipe B will fill it in x+6 hours<br />
1/x + 1/x+6=1/4<br />
Solving this we get x=6.<br />
Hence, A takes 6 hours to fill the cistern separately.<br />
<br />
5)A tank is filled by 3 pipes with uniform flow. The first two pipes<br />
operating simultaneously fill the tan in the same time during which<br />
the tank is filled by the third pipe alone. The 2nd pipe fills the tank<br />
5 hours faster than first pipe and 4 hours slower than third pipe. The<br />
time required by first pipe is :<br />
<br />
Sol: Suppose, first pipe take x hours to fill the tank then<br />
B & C will take (x-5) and (x-9) hours respectively.<br />
Therefore, 1/x +1/(x-5) =1/(x-9)<br />
On solving, x=15<br />
Hence, time required by first pipe is 15 hours.<br />
<br />
6)A large tanker can be filled by two pipes A& B in 60min and 40 min<br />
respectively. How many minutes will it take to fill the tanker from<br />
empty state if B is used for half the time & A and B fill it together for<br />
the other half?<br />
<br />
Sol: Part filled by (A+B) n 1 min=(1/60 +1/40)=1/24<br />
Suppose the tank is filled in x minutes<br />
Then, x/2(1/24+1/40)=1<br />
=> (x/2)*(1/15)=1<br />
=> x=30 min.<br />
<br />
7)Two pipes A and B can fill a tank in 6 hours and 4 hours respectively.<br />
If they are opened on alternate hours and if pipe A s opened first, in<br />
how many hours, the tank shall be full.<br />
<br />
Sol: (A+B)’s 2 hours work when opened alternatively =1/6+1/4 =5/12<br />
(A+B)’s 4 hours work when opened alternatively=10/12=5/6<br />
Remaining part=1 -5/6=1/6.<br />
Now, it is A’s turn and 1/6 part is filled by A in 1 hour.<br />
So, total time taken to fill the tank=(4+1)= 5 hours.<br />
<br />
8)Three taps A,B and C can fill a tank in 12, 15 and 20 hours respectively.<br />
If A is open all the time and B and C are open for one hour each<br />
alternatively, the tank will be full in.<br />
<br />
Sol: (A+B)’s 1 hour’s work=1/12+1/15=9/60=3/20<br />
(A+C)’s 1 hour’s work=1/20+1/12=8/60=2/15<br />
Part filled in 2 hours=3/20+2/15=17/60<br />
Part filled in 2 hours=3/20+2/15= 17/60<br />
Part filled in 6 hours=3*17/60 =17/20<br />
Remaining part=1 -17/20=3/20<br />
Now, it is the turn of A & B and 3/20 part is filled by A& B in 1 hour.<br />
Therefore, total time taken to fill the tank=6+1=7 hours<br />
<br />
9)A Booster pump can be used for filling as well as for emptying a tank.<br />
The capacity of the tank is 2400 m3. The emptying capacity of the tank is<br />
10 m3 per minute higher than its filling capacity and the pump needs 8<br />
minutes lesser to empty the tank than it needs to fill it. What is the<br />
filling capacity of the pump?<br />
<br />
Sol: Let, the filling capacity of the pump be x m3/min<br />
Then, emptying capacity of the pump=(x+10) m3/min.<br />
So,2400/x – 2400/(x+10) = 8<br />
on solving x=50.</b></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-16262849766221481982011-04-17T08:51:00.000-07:002011-04-23T22:24:16.890-07:00Idioms<div dir="ltr" style="text-align: left;" trbidi="on"><span class="style1"><strong><span style="color: black;">A Bird In The Hand Is Worth Two In The Bush: </span></strong></span><span class="style2"><br />
<span style="color: black;">Having something that is certain is much better than taking a risk for more, because chances are you might lose everything.<br />
</span><strong><span><span style="color: black;"><span class="style1">A Blessing In Disguise: </span></span></span></strong><span style="color: black;">Something good that isn't recognized at first. <br />
</span><strong><span><span style="color: black;"><span class="style1">A Chip On Your Shoulder: </span></span></span></strong><span style="color: black;">Being upset for something that happened in the past. <br />
</span><span style="color: black;"><span><strong><span class="style1">A Dime A Dozen: </span></strong>Anything that is common and easy to get.</span></span></span><br />
<br />
<span class="style2"><span style="color: black;">For More Idioms Visit <a href="http://www.idiomsite.com/">http://www.idiomsite.com/</a></span></span><br />
<br />
</div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-67584718762666108862011-04-04T03:53:00.001-07:002011-04-04T03:53:49.255-07:00Compound Interest<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: center;"><span style="color: red; font-size: large;"><strong>Compound Interest</strong></span></div><div style="text-align: center;"><br />
</div><div class="MsoNormal"><b>Compound Interest: </b>sometimes it so happens that the borrower and the lender agree to fix up a certain unit of time, say <i>yearly or half-yearly or quarterly</i> to settle the previous amount.</div><div class="MsoNormal"><span style="mso-tab-count: 1;"> </span>In such case, the amount after first unit of time becomes the principal for the second unit, the amount after second unit becomes the principal for the third unit and so on.</div><div class="MsoNormal"><span style="mso-tab-count: 1;"> </span>After a specified period, <i>the difference between the amount and the money borrowed is called the </i><b>compound Interest</b><i> (abbreviated as C.I.) for that period.</i></div><div class="MsoNormal"> <b><span style="color: green;">FORMULAE:</span></b></div><b><span style="mso-spacerun: yes;"> </span></b>Let <b>Principal</b> =p, <b>Rate</b> = R% per annum, <b>Time</b>=n years<br />
<div style="margin-left: 0.75in; mso-list: l0 level1 lfo1; tab-stops: list .75in; text-indent: -0.5in;"><b>I.<span style="font: 7pt "Times New Roman";"> </span>When interest is compounded annually: </b></div><div style="margin-left: 1.5in;">Amount = P[ 1 + (R/100)]<sup>n</sup><sup><span style="mso-spacerun: yes;"> </span></sup></div><div style="margin-left: 0.75in; mso-list: l0 level1 lfo1; tab-stops: list .75in; text-indent: -0.5in;"><b>II.<span style="font: 7pt "Times New Roman";"> </span>When the interest is compounded half-yearly : </b></div><div style="margin-left: 0.25in;"><b><span style="mso-spacerun: yes;"> </span></b>Amount = p[ 1 + (R/2)/100]<sup>2n</sup><sup> </sup></div><div style="margin-left: 0.75in; mso-list: l0 level1 lfo1; tab-stops: list .75in; text-indent: -0.5in;"><b>III.<span style="font: 7pt "Times New Roman";"> </span>When the interest is compounded quarterly : </b></div><div style="margin-left: 0.25in;"><b><span style="mso-spacerun: yes;"> </span></b>Amount = P[ 1 + (R/4)/100 ]<sup>4n </sup></div><div style="margin-left: 0.25in;"><b>IV.</b><span style="font: 7pt "Times New Roman";"> </span>When the interest is compounded annually but time is in fraction, say<b>3 2/5 Years.<span style="mso-spacerun: yes;"> </span></b></div><div style="margin-left: 0.25in;"><b><span style="mso-spacerun: yes;"> </span></b>Amount = P{ [1 + (R/100)]<sup>3<b><span style="mso-spacerun: yes;"> </span></b></sup>x [ 1 + (2R/5)/100] }</div><div style="margin-left: 0.25in;"><b>V.<span style="font-family: Times New Roman; font-size: 7pt; font-style: normal; font-variant: normal;"> </span></b><span style="font: 7pt "Times New Roman";"> </span>When rates are different for different years, say R<sub>1</sub>%, R<sub>2</sub>%, R<sub>3</sub>% for 1<sup>st</sup>,<span style="mso-spacerun: yes;"> </span><b><span style="mso-spacerun: yes;"> </span>2<sup>nd</sup><span style="mso-spacerun: yes;"> </span>and 3<sup>rd</sup> year respectively. </b></div><div style="margin-left: 0.25in;"><b><span style="mso-spacerun: yes;"> </span></b>Then, Amount= P [ 1 + R<sub>1</sub>/100][ 1 + R<sub>2</sub>/100][ 1+ R<sub>3</sub>/100]</div><div style="margin-left: 0.25in;"><b>VI.</b><span style="font: 7pt "Times New Roman";"> </span>Present worth of Rs. X Due n years hence is given by :</div><div style="margin-left: 0.25in;"><b><span style="mso-spacerun: yes;"> </span></b><span style="mso-spacerun: yes;"> </span>Present worth = X/ (1 + R/100)<sup>n </sup></div><div style="margin-left: 0.25in;"><sup> </sup></div><div style="margin-left: 0.25in;"><span style="mso-spacerun: yes;"> </span><b>Solved Problem</b></div><div align="left" style="margin-left: 0px;"><b>Ex.1. <i>Find compound interest on Rs.6250 at 16% per annum for 2 years, compounded annually. </i></b></div><div align="left" style="margin-left: 0px;"><b> Sol.<span style="mso-spacerun: yes;"> </span></b>Amount = Rs. [ 6250 x ( 1 + 16/100)<sup>2</sup> ]</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span>=<span style="mso-spacerun: yes;"> </span>Rs.</b>[ 6250 x 29/25 x 29/25 ] = Rs.8410.</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span>.</b>. C.I = Rs.(8410 – 6250) = Rs. 2160.</div><div align="left" style="margin-left: 0px;"> <b>Ex.2. <i>Find compound interest on Rs. 5000 at 12% per annum for 1 year,<span style="mso-spacerun: yes;"> </span></i><i>compounded<span style="mso-spacerun: yes;"> </span>half-yearly.</i></b></div><div align="left" style="margin-left: 0px;"><b>Sol</b><i>.</i><span style="mso-spacerun: yes;"> </span>Principal = Rs.5000, Rate=6% per half year</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span></b>Time = 1 year<span style="mso-spacerun: yes;"> </span>= 2 half-<i>years</i></div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>Amount = Rs. {5000 x ( 1 + 6/100)<sup>2</sup>]<i> </i>= Rs. [ 5000 x 53/50 x 53/50 ]</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>= Rs. 5618</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>.. C.I. = Rs. (5618 – 5000) = Rs. 618</div><div align="left" style="margin-left: 0px;"> <b>Ex.3. <i>Find compound interest on Rs. 16000 at 20% per annum for 9 months,</i><i>compounded quarterly.</i></b><span style="mso-spacerun: yes;"> </span></div><div align="left" style="margin-left: 0px;"><b>Sol.<span style="mso-spacerun: yes;"> </span></b>Principal = Rs. 16000,<span style="mso-spacerun: yes;"> </span>Time = 9 months = 3 quarters</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span></b>Rate = 20% per annum = 5% per quarter.</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>.. Amount = Rs. [ 16000 x { 1 + 5/100 )<sup>3 </sup>]</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>= Rs. [ 16000 x 21/20 x 21/20 x 21/20 ] = Rs. 18522.</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>.. C.I. = Rs. (18522 – 16000) = Rs. 2522.</div><div align="left" style="margin-left: 0px;"> <b>Ex.4. <i><span style="mso-spacerun: yes;"> </span>The difference between the compounded interest and simple interest on a certain sum at 10% per annum for 2 years is Rs.631. Find the sum. </i></b></div><div align="left" style="margin-left: 0px;"><b>Sol. </b>Let the sum be Rs. X .Then,</div><div align="left" style="margin-left: 0px;"><b><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>C.</b>I.. = <i>x</i>[ 1 + 10/100 ]<sup>2 </sup><span style="mso-spacerun: yes;"> </span>- <i>x </i>] = 21<i>x</i>/100</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span>S.</b>I.<span style="mso-spacerun: yes;"> </span>= [ (<i>X</i>x10x2)/100] = <i>X</i>/5</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span>.</b>. (C.I.) – (S.I.) = [ (21x)/100 – (x/5) ] = x/100</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span>.</b>. x/100 = 631<span style="mso-spacerun: yes;"> </span>x= 63100</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span></b>Hence, the sum is Rs. 63100</div><div align="left" style="margin-left: 0px;"> <b>Ex.5. <i>If the compound interest on a certain sum for 2 years at 12% per annum is<span style="mso-spacerun: yes;"> </span></i><span style="mso-spacerun: yes;"> </span><i>Rs. 1590, what would be the simple interest? </i></b></div><div align="left" style="margin-left: 0px;"><b>Sol. </b>Let the sum be Rs. X. Then</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span></b><span style="mso-spacerun: yes;"> </span>X{ 1 + 12/100 }<sup>2</sup> – X = 1590<span style="mso-spacerun: yes;"> </span>or<span style="mso-spacerun: yes;"> </span>(784X/625) – X = 1590</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>Or 159X/625 = 1590 or x = {1590 x 625}/159 =6250</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>.. Sum = Rs. 6250</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>.. S.I. = Rs. [ (6250 x 12 x 2)/100] = Rs. 1500</div><div align="left" style="margin-left: 0px;"> <b>Ex.6. <i>A sun of money amounts to Rs.6690 after 3 years and to Rs 10035 after 6 </i><span style="mso-spacerun: yes;"> </span><i>years on compound interest. Find the sum. </i></b></div><div align="left" style="margin-left: 0px;"><b><i><span style="mso-spacerun: yes;"> </span></i></b><span style="mso-spacerun: yes;"> </span>P{ 1 + R/100 }<sup>3</sup> = 6690 ….(i)<span style="mso-spacerun: yes;"> </span>and<span style="mso-spacerun: yes;"> </span>P{ 1 + R/100 }<sup>6 </sup><span style="mso-spacerun: yes;"> </span>= 10035<span style="mso-spacerun: yes;"> </span>… (ii)</div><div align="left" style="margin-left: 0px;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>On Dividing, we get [ 1 + R/100 ]<sup>3 </sup>= 10035/6690 = 3/2</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>Substituting this value in (i), we get;</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>P x 3/2 =6690<span style="mso-spacerun: yes;"> </span>or<span style="mso-spacerun: yes;"> </span>P=[6690 x 2/3] = 4460</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>Hence, the sum is Rs. 4460 </div><div align="left" style="margin-left: 0px;"><b>Ex.7. <i>A sum of money doubles itself at compound interest in 15 years. In how many </i><span style="mso-spacerun: yes;"> </span><i>years will it become eight times? </i></b></div><div align="left" style="margin-left: 0px;"><b>Sol.<span style="mso-spacerun: yes;"> </span></b><span style="mso-spacerun: yes;"> </span>P { 1 + R/100 }<sup>15 </sup>= 2P<span style="mso-spacerun: yes;"> </span>ie 2P= [ 1 + R/100]<sup>15</sup> = 2<span style="mso-spacerun: yes;"> </span>… (i</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span></b>Let<span style="mso-spacerun: yes;"> </span>P[ 1 + R/100]n = 8P<span style="mso-spacerun: yes;"> </span>[ 1 + R/100]<sup>n</sup> =8 = 2<sup>3</sup> = { [1 + R/100]<sup>15</sup> }<sup>3</sup></div><div align="left" style="margin-left: 0px;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>[ 1 + R/100]<sup>n</sup> = [ 1 + R/100]<sup>45</sup></div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>i.e n=45</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>Thus required time = 45 years</div><div align="left" style="margin-left: 0px;"><b>Ex.8. <i>A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years . Find </i></b><b><span style="mso-spacerun: yes;"> </span><i>the sum and rate per cent. </i></b></div><div align="left" style="margin-left: 0px;"><b>Sol.<span style="mso-spacerun: yes;"> </span></b>S.I. on Rs.7350 for 1 year = Rs.(8575 – 7350) = Rs.1225.</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span>.<i>. </i></b>Rate = [(100 x 1225)/(7350 x 1)]% = 16 2/3%</div><div align="left" style="margin-left: 0px;"><b><span style="mso-spacerun: yes;"> </span></b>Let the sum be Rs. X .Then</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>X[1 + 50/(3 x100)]2 = 7350<span style="mso-spacerun: yes;"> </span></div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>i.e X x 7/6 x 7/6 =7350</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>X= {7350 x 36/49]</div><div align="left" style="margin-left: 0px;"><span style="mso-spacerun: yes;"> </span>.. Sum = Rs. 5400</div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-35987460020152433712011-03-30T07:08:00.000-07:002011-03-30T07:08:20.728-07:00Number Word Problems<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-family: Arial;"><strong><em><span style="color: purple; font-size: large;">Number Word Problems</span></em></strong></span><br />
<strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">Number" word problems are fairly contrived, but they're also fairly standard, so you should learn how to handle them. After all, the point of these problems isn't their relation to "real life", but your ability to extract the math from the English.</span> </span></span></strong><br />
<ul><li><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: green;">The sum of two consecutive integers is </span><span style="color: green;">15</span><span style="color: green;">. Find the numbers.</span> </span></span></strong></li>
</ul><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">They've given me two pieces of information here. First, I know that I am adding two numbers, and their sum is fifteen. Second, I know that the numbers are nice neat round numbers (like </span><span style="color: black;">–3</span><span style="color: black;"> or </span><span style="color: black;">6</span><span style="color: black;">), not messy ones (like </span><span style="color: black;">–4.628</span><span style="color: black;"> or</span><span style="color: black;"> <sup>17</sup>/<sub>32</sub></span><span style="color: black;">), and that the second number is one more than the first. This last piece of information comes from the fact that "consecutive integers" (or "consecutive whole numbers", if they're restricting the possibilities to only positive numbers) are one unit apart. Examples of "consecutive integers" would be </span><span style="color: black;">–12</span><span style="color: black;"> and </span><span style="color: black;">–11</span><span style="color: black;">, </span><span style="color: black;">1</span><span style="color: black;"> and </span><span style="color: black;">2</span><span style="color: black;">, and </span><span style="color: black;">99</span><span style="color: black;"> and </span><span style="color: black;">100</span><span style="color: black;">. Using these facts, I can set up the </span></span></span></strong><a href="http://www.purplemath.com/modules/translat.htm"><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><strong>translation</strong></span></a><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">.</span> <span style="color: black;">I will represent the first number by "</span><span style="color: black;"><i>n</i></span><span style="color: black;">". Then the second number has to be "</span><span style="color: black;"><i>n</i> + 1</span><span style="color: black;">". Their sum is then:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;"><i>n</i> + (<i>n</i> + 1) = 15</span><span style="color: black;"> </span><span style="color: black;">2<i>n</i> + 1 = 15</span><span style="color: black;"> </span><span style="color: black;">2<i>n</i> = 14</span><span style="color: black;"> </span><span style="color: black;"><i>n</i> = 7</span><span style="color: black;"> </span><span style="color: white;"> Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved</span></span></span></strong></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">The exercise did not ask me for the value of the variable </span><span style="color: black;"><i>n</i></span><span style="color: black;">; it asked for the identity of two numbers. So my answer is not "</span><span style="color: black;"><i>n</i> = 7</span><span style="color: black;">"; the actual answer is:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: purple;">"The numbers are </span><span style="color: purple;">7</span><span style="color: purple;"> and </span><span style="color: purple;">8</span><span style="color: purple;">."</span></span></span></strong></ul></ul><ul><li><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: green;">The product of two consecutive negative even integers is </span><span style="color: green;">24</span><span style="color: green;">. Find the numbers.</span> </span></span></strong></li>
</ul><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">They have told me quite a bit about these two numbers: the numbers are even and they are negative. (The fact that they are negative may help if I come up with two solutions — a positive and a negative — so I'll know which one to pick.) Since even numbers are two apart (for example, </span><span style="color: black;">–4</span><span style="color: black;"> and </span><span style="color: black;">–2</span><span style="color: black;"> or</span><span style="color: black;"> 10</span><span style="color: black;"> and </span><span style="color: black;">12</span><span style="color: black;">), then I also know that the second number is two greater than the first. I also know that, when I multiply the two numbers, I will get </span><span style="color: black;">24</span><span style="color: black;">. In other words, letting the first number be "</span><span style="color: black;"><i>n</i></span><span style="color: black;">" and the second number be "</span><span style="color: black;"><i>n</i> + 2</span><span style="color: black;">", I have:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">(<i>n</i>)(<i>n</i> + 2) = 24</span><span style="color: black;"> </span><span style="color: black;"><i>n</i><sup>2</sup> + 2<i>n</i> = 24</span><span style="color: black;"> </span><span style="color: black;"><i>n</i><sup>2</sup> + 2<i>n</i> – 24 = 0</span><span style="color: black;"> </span><span style="color: black;">(<i>n</i> + 6)(<i>n</i> – 4) = 0</span><span style="color: black;"> </span></span></span></strong></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">Then the solutions are </span><span style="color: black;"><i>n</i> = –6</span><span style="color: black;"> and </span><span style="color: black;"><i>n</i> = 4</span><span style="color: black;">. Since the numbers I am looking for are negative, I can ignore the "</span><span style="color: black;">4</span><span style="color: black;">" and take </span><span style="color: black;"><i>n</i> = –6</span><span style="color: black;">. Then the next number is </span><span style="color: black;"><i>n</i> + 2 = –4</span><span style="color: black;">, and the answer is</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: purple;">The numbers are </span><span style="color: purple;">–6</span><span style="color: purple;"> and </span><span style="color: purple;">–4</span><span style="color: purple;">.</span></span></span></strong></ul></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">In the exercise above, one of the answers was one of the solutions to the equation; the other answer was the negative of the other solution to the equation. Warning: Do not assume that you can use both solutions if you just change the signs to be whatever you feel like. While this often "works", it does not <i>always</i> work, and it's sure to annoy your teacher. Throw out invalid results, and solve properly for valid ones.</span> </span></span></strong><br />
<ul><li><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: green;">Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is </span><span style="color: green;">71</span><span style="color: green;">. What are the numbers?</span> </span></span></strong></li>
</ul><span style="color: black; font-family: Arial, Helvetica, sans-serif; font-size: large;"><strong>The point of exercises like this is to give you practice in unwrapping and unwinding these words, and turning the words into algebraic equations. The point is in the solving, not in the relative "reality" of the problem. That said, how do you solve this? The best first step is to start labelling:</strong></span><br />
<ul><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">the larger number: </span><i><span style="color: black;">x</span></i><span style="color: black;"> </span><span style="color: black;">the smaller number: </span><i><span style="color: black;">y</span></i><span style="color: black;"> </span><span style="color: black;">twice the larger: </span><span style="color: black;">2</span><i><span style="color: black;">x</span></i><span style="color: black;"> </span><span style="color: black;">three more than five times the smaller: </span><span style="color: black;">5</span><i><span style="color: black;">y</span></i><span style="color: black;"> + 3</span><span style="color: black;"> </span><span style="color: black;">relationship between ("is"): </span><span style="color: black;">2</span><i><span style="color: black;">x</span></i><span style="color: black;"> = 5</span><i><span style="color: black;">y</span></i><span style="color: black;"> + 3</span><span style="color: black;"> </span><span style="color: black;">four times the larger: </span><span style="color: black;">4</span><i><span style="color: black;">x</span></i><span style="color: black;"> </span><span style="color: black;">three times the smaller: </span><span style="color: black;">3</span><i><span style="color: black;">y</span></i><span style="color: black;"> </span><span style="color: black;">relationship between ("sum of"): </span><span style="color: black;">4</span><i><span style="color: black;">x</span></i><span style="color: black;"> + 3</span><i><span style="color: black;">y</span></i><span style="color: black;"> = 71</span><span style="color: black;"> </span></span></span></strong></ul></ul><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">Now I have two equations in two variables:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">2<i>x</i> = 5<i>y</i> + 3</span><span style="color: black;"> </span><span style="color: black;">4<i>x</i> + 3<i>y</i> = 71</span><span style="color: black;"> </span></span></span></strong></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">I will solve, say, the first equation for </span><i><span style="color: black;">x</span></i><span style="color: black;">:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><i><span style="color: black;">x</span></i><span style="color: black;"> = (5/2)</span><i><span style="color: black;">y</span></i><span style="color: black;"> + (3/2)</span></span></span></strong></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">Then I'll plug the right-hand side of this into the second equation in place of the "</span><i><span style="color: black;">x</span></i><span style="color: black;">":</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">4[ (5/2)<i>y</i> + (3/2) ] + 3<i>y</i> = 71</span><span style="color: black;"> </span><span style="color: black;">10<i>y</i> + 6 + 3<i>y</i> = 71</span><span style="color: black;"> </span><span style="color: black;">13<i>y</i> + 6 = 71</span><span style="color: black;"> </span><span style="color: black;">13<i>y</i> = 65</span><span style="color: black;"> </span><span style="color: black;"><i>y</i> = 65/13 = 5</span><span style="color: black;"> </span></span></span></strong></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">Now that I have the value for </span><span style="color: black;"><i>y</i></span><span style="color: black;">, I can solve for </span><i><span style="color: black;">x</span></i><span style="color: black;">:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;"><i>x</i> = (5/2)<i>y</i> + (3/2)</span><span style="color: black;"> </span><span style="color: black;"><i>x</i> = (5/2)(5) + (3/2)</span><span style="color: black;"> </span><span style="color: black;"><i>x</i> = (25/2) + (3/2)</span><span style="color: black;"> </span><span style="color: black;"><i>x</i> = 28/2 = 14</span><span style="color: black;"> </span></span></span></strong></ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;">As always, I need to remember to answer the question that was actually asked. The solution here is not "</span><span style="color: black;"><i>x</i> = 14</span><span style="color: black;">", but is the following sentence:</span> </span></span></strong><ul><strong><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: purple;">The larger number is </span><span style="color: purple;">14</span><span style="color: purple;">, and the smaller number is </span><span style="color: purple;">5</span><span style="color: purple;">.</span></span></span></strong></ul></ul><span style="color: black; font-family: Arial, Helvetica, sans-serif; font-size: large;"><strong>The trick to doing this type of problem is to label everything very explicitly. Until you become used to doing these, do not attempt to keep track of things in your head. Do as I did in this last example: clearly label every single step. When you do this, these problems generally work out rather easily.</strong></span></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-2687542635657785402011-03-26T01:44:00.000-07:002011-03-26T01:44:59.048-07:00Types of Prepositions with example<div dir="ltr" style="text-align: left;" trbidi="on">What are the different types of Preposition?<br />
<br />
<strong>Preposition of place</strong><br />
<strong>Preposition of time</strong><br />
<strong>Preposition of movement</strong><br />
<br />
Preposition of <strong>place</strong> - at, on, in, below, beside, under, behind, between<br />
Prepositions of place are used to describe the place or position of nouns.<br />
<br />
Example<br />
1.The dog is in the garden.<br />
2.The box is behind the door<br />
3. He threw the ball over the roof <br />
4. She lives near the school.<br />
5. The house is between 3rd Street and 4th Street.<br />
6. London is on the river Thames. <br />
<br />
Preposition of <strong>time-</strong>at, on, in, during,<br />
Prepositions of time- used to show when something happened.<br />
<br />
More examples: since, for, by, from -to, from-until, during, in.<br />
1. I haven’t seen her since yesterday.<br />
2. I'm leaving to Chennai in a week.<br />
4. I waited for him from 8 a.m. until 10 a.m., and later went out<br />
5. I watch TV during the evening. <br />
<br />
Preposition of <strong>Movement</strong><br />
Preposition of Movement is used to show movement.<br />
<br />
Example: to, towards, through, across, over, into, onto <br />
To: signifies movement toward a specific destination.<br />
Example: He went to the park.<br />
Towards: suggests movement in a general direction,<br />
Example: The helicopter flew towards south.<br />
Into: Suji fell into the well.<br />
Onto: Clara jumped onto the bench. </div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-62252239122499122742011-03-26T01:36:00.000-07:002011-03-26T01:36:18.832-07:00Articles usage in english<div dir="ltr" style="text-align: left;" trbidi="on"><h1>A, An or The?</h1>When do we say "<b>the</b> dog" and when do we say "<b>a</b> dog"? (On this page we talk only about singular, countable nouns.)<br />
<b>The</b> and <b>a/an</b> are called "articles". We divide them into "definite" and "indefinite" like this:<br />
<br />
<table border="1" cellpadding="5" cellspacing="0"><tbody>
<tr><td align="center" colspan="2">Articles</td></tr>
<tr><td align="center"><b>Definite</b></td><td align="center"><b>Indefinite</b></td></tr>
<tr><td align="center">the</td><td align="center">a, an</td></tr>
</tbody></table><br />
We use "definite" to mean sure, certain. "Definite" is particular.<br />
We use "indefinite" to mean not sure, not certain. "Indefinite" is general.<br />
When we are talking about one thing in particular, we use <b>the</b>. When we are talking about one thing in general, we use <b>a</b> or <b>an</b>.<br />
Think of the sky at night. In the sky we see 1 moon and millions of stars. So normally we would say:<br />
<ul><li>I saw <b>the</b> moon last night. </li>
<li>I saw <b>a</b> star last night.</li>
</ul>Look at these examples:<br />
<br />
<table border="1" cellpadding="5" cellspacing="0"><tbody>
<tr><td><b>the</b></td><td><b>a, an</b></td></tr>
<tr><td><ul><li><b>The</b> capital of France is Paris. </li>
<li>I have found <b>the</b> book that I lost. </li>
<li>Have you cleaned <b>the</b> car? </li>
<li>There are six eggs in <b>the</b> fridge. </li>
<li>Please switch off <b>the</b> TV when you finish.</li>
</ul></td><td><ul><li>I was born in <b>a</b> town. </li>
<li>John had <b>an</b> omelette for lunch. </li>
<li>James Bond ordered <b>a</b> drink. </li>
<li>We want to buy <b>an</b> umbrella. </li>
<li>Have you got <b>a</b> pen?</li>
</ul></td></tr>
</tbody></table><br />
Of course, often we can use <b>the</b> or <b>a/an</b> for the same word. It depends on the situation, not the word. Look at these examples:<br />
<ul><li>We want to buy <b>an</b> umbrella. (Any umbrella, not a particular umbrella.) </li>
<li>Where is <b>the</b> umbrella? (We already have an umbrella. We are looking for our umbrella, a particular umbrella.)</li>
</ul><div class="ECtip">This little story should help you understand the difference between <b>the</b> and <b>a, an</b>:<br />
<br />
<b>A</b> man and <b>a</b> woman were walking in Oxford Street. <b>The</b> woman saw <b>a</b> dress that she liked in <b>a</b> shop. She asked <b>the</b> man if he could buy <b>the</b> dress for her. He said: "Do you think <b>the</b> shop will accept <b>a</b> cheque? I don't have <b>a</b> credit card."</div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-15667274381594491822011-03-21T02:26:00.000-07:002011-03-21T02:38:44.336-07:00Number series<div dir="ltr" style="text-align: left;" trbidi="on"><strong> 1.Prime Number Series<br />
<br />
Example:<br />
2,3,5,7,11,..............<br />
<br />
2.Even Number Series<br />
Example:<br />
2,4,6,8,10,12,...........<br />
<br />
3.Odd Number Series:<br />
<br />
Example:<br />
1,3,5,7,9,11,...........<br />
4.<span class="IL_AD" id="IL_AD8"><u><span style="color: #cc0000; font-family: Tahoma;">Perfect Squares</span></u></span>:<br />
<br />
Example:<br />
1,4,9,16,25,............<br />
<br />
5.Perfect Cubes:<br />
<br />
Example:<br />
1,8,27,64,125,.................<br />
<br />
.Multiples of Number Series: <br />
<br />
Example:<br />
<br />
3,6,9,12,15,..............are multiples of 3<br />
<br />
7.Numbers in Arthimetic Progression(A.P):<br />
<br />
Example:<br />
13,11,9,7................<br />
<br />
8.Numbers in G.P:<br />
Example:<br />
<br />
48,12,3,.....</strong></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-45529892731687031232011-03-21T02:12:00.001-07:002011-03-21T02:17:42.996-07:00Problems On Ages<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: center;"><span style="color: blue; font-size: large;"><strong>Problems On Ages</strong></span> </div> <br />
<b>1. The Ratio of Ages of Mona and Sona is 4:5. Twelve Years hence, their ages will be in the ratio of 5:6. What will be Sona's age after 6 years ?</b> <br />
<div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>Sol:</b> Let their present ages be 4x & 6x </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Then (4x + 12)/(5x + 12) = 5/6 or x=12 </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Sona's age after 6 years = (5x +6) = 66 years</div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>2.Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What their present ages ?</b> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>Sol :</b> Let son's age 8 years ago be x years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Then Ramu's age at that time = 4x years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Son's age after 8 years = (x +8) + 8 = (x + 16) years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Ramu's age after 8 years = (4x + 8) + 8 = (4x + 16) years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> 2(x + 16) = 4x + 16 or x=8 </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Son's present age = (x + 8) = 16 years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Ramu's present age= (4x + 8) = 40 years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>3. A man is four times as old as his son. Five years ago, the man was nine times as old his son was at that time. What is the present age of a man ?</b> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>Sol : </b>Let son's age = x, then man's age =4x. </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> 9(x - 5) = (4x-5) or x=8. </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Man's present age = (4x + 7) = 35 years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>4. The sum of ages of Aruna and her mother is 49 years. Also, 7 years ago, the mothers age was 4 times Aruna's age. Find the present age of Aruna's mother</b>. </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>Sol : </b>Let Aruna's age 7 years ago be x. </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Mother's age 7 years ago = 4x </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> (x + 7) + (4x + 7) =49 or x=7 </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> Mother's present age = (4x + 7) = 35 years </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>5. The ages of A and B differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.</b> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"><b>Sol :</b> Let A's age = x & B's age = (x + 16) </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> 3(x - 6) = (x + 16 - 6) or x=14 </div><div style="line-height: 100%; margin-bottom: 0px; margin-top: 0px;"> A's age = 14 years & B's age = 30 years. <br />
<span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;">6. </b>The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is:</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>a. 5 : 2<span style="mso-tab-count: 3;"> </span><b style="mso-bidi-font-weight: normal;">b. 7 : 3</b><span style="mso-tab-count: 3;"> </span>c. 9 : 2<span style="mso-tab-count: 3;"> </span>d. 13 : 4</div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b> <br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">Let the<span style="mso-spacerun: yes;"> </span>father age be x years</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">Let the son’s age be y years</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">Given : 10 years ago, father age was thrice son age</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="mso-tab-count: 1;"> </span>X – 10 = 3 (y – 10)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="mso-tab-count: 1;"> </span>x- 3y = -30 +10</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="mso-tab-count: 1;"> </span>x-3y = - 20 ---------------- (1)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">Given : 10 years after, father age was twice son age</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;">X + 10 = 2 (y + 10)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;">X – 2y = 10 -----------------(2)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">To find : Ratio of present age (x : y = ?)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;">To get y value subtract (2) from (1)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;">Y = 30 ; substitute this value in (1) we will get x value</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;">X = 70</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;">70 : 30</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;"><b style="mso-bidi-font-weight: normal;">7 : 3</b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span></b><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><strong>7.</strong> The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>a. 31<span style="mso-tab-count: 3;"> </span>b. 36<span style="mso-tab-count: 3;"> </span><b style="mso-bidi-font-weight: normal;">c. 51<span style="mso-tab-count: 1;"> </span></b><span style="mso-tab-count: 2;"> </span>d. None of these</div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b> <br />
<div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">36<span style="mso-spacerun: yes;"> </span>= 14</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">37 = 15 (teacher’s age included then average increased<span style="mso-spacerun: yes;"> </span>by one<span style="mso-spacerun: yes;"> </span>; ie =15)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">To find :</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">Teacher’s age:</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify; text-indent: 0.5in;">(37 – 36) 15 = (15-14) (36)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify; text-indent: 0.5in;">15 + 36</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify; text-indent: 0.5in;"><b style="mso-bidi-font-weight: normal;">51 years</b></div><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">8. If 6 years are subtracted from the present age of Gulzar and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Mahesh whose age is 5 years, then what is the present age of Gulzar?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">Answer : 60</span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b> <br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of Gulzar be x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of Anup be y years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of<span style="mso-spacerun: yes;"> </span>Mahesh be z years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given: <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><stroke joinstyle="miter"></stroke><formulas><f eqn="if lineDrawn pixelLineWidth 0"></f><f eqn="sum @0 1 0"></f><f eqn="sum 0 0 @1"></f><f eqn="prod @2 1 2"></f><f eqn="prod @3 21600 pixelWidth"></f><f eqn="prod @3 21600 pixelHeight"></f><f eqn="sum @0 0 1"></f><f eqn="prod @6 1 2"></f><f eqn="prod @7 21600 pixelWidth"></f><f eqn="sum @8 21600 0"></f><f eqn="prod @7 21600 pixelHeight"></f><f eqn="sum @10 21600 0"></f></formulas><path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"></path><lock aspectratio="t" v:ext="edit"></lock></shapetype><shape id="_x0000_i1025" o:ole="" style="height: 30.75pt; width: 29.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>= y</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;"><span style="font-size: 14pt; line-height: 150%;">X – 6 = 18y</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; text-align: justify; text-indent: 0.5in;"><span style="font-size: 14pt; line-height: 150%;">X – 18y = 6</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : Anup is 2 years younger to Mahesh</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Y = z – 2</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : Mahesh age is 5 years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Z = 5</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1026" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image005.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>y = 5 - 2 ; y = 3</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1027" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>x – 18 (3) = 6 ; X – 54 = 6 ; X = 6 + 54</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X = 60</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find : Present age of gulzar</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">X<span style="mso-spacerun: yes;"> </span>=<span style="mso-spacerun: yes;"> </span>60 years</span></b></div><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">9. The average age of five members of a family is 21 years. If the age of the grandfather be included, the average is increased by 9 years. The age of the grandfather is :</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">Answer : 75</span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: 0in; text-align: justify;"><rect id="_x0000_s1036" style="height: 13.7pt; left: 0px; margin-left: 405pt; margin-top: 2.4pt; position: absolute; text-align: left; width: 27pt; z-index: 251703808;"></rect><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : </span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Number of members<span style="mso-tab-count: 3;"> </span>Average</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 2;"> </span>5<span style="mso-tab-count: 5;"> </span>21</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 2;"> </span>5 +1<span style="mso-tab-count: 5;"> </span>21 + 9<span style="mso-tab-count: 2;"> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>5 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1028" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image008.wmz"></imagedata></shape></span><span style="mso-tab-count: 1;"> </span>21</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>6 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1029" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image010.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>30</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find : Grand father’s age</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Grand father age = (6-5) (30) + (30-21) (5)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 4;"> </span>=<span style="mso-tab-count: 1;"> </span>30 + 45 </span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 4;"> </span>=<span style="mso-tab-count: 1;"> </span>75 </span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span></b><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">10. The average age of a n adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The originals strength of the class was: </span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">Answer : 12</span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Mean = <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1030" o:ole="" style="height: 33.75pt; width: 26.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image011.wmz"></imagedata></shape></span></span></b><br />
<div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let </span><span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1031" o:ole="" style="height: 20.25pt; width: 24pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image013.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>be the sum of the ages of n adults</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">Let <span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1032" o:ole="" style="height: 20.25pt; width: 24.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image015.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>be the sum of the ages of 12 students</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;">Given : <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1033" o:ole="" style="height: 17.25pt; width: 9.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image017.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>=<span style="mso-spacerun: yes;"> </span><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1034" o:ole="" style="height: 33.75pt; width: 26.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image019.wmz"></imagedata></shape></span></span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">40 = <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1035" o:ole="" style="height: 33.75pt; width: 26.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image011.wmz"></imagedata></shape></span></span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">40 n = </span><span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1036" o:ole="" style="height: 20.25pt; width: 24pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image013.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>--------------------(1)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="mso-text-raise: -5.0pt; position: relative; top: 5pt;"><shape id="_x0000_i1037" o:ole="" style="height: 18.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image021.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>= <b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1038" o:ole="" style="height: 33.75pt; width: 27pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image023.wmz"></imagedata></shape></span></span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">32 = <span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1039" o:ole="" style="height: 33.75pt; width: 27pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image025.wmz"></imagedata></shape></span></span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">32 x 12 = </span></b><span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1040" o:ole="" style="height: 20.25pt; width: 24.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image015.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1041" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image027.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>384 = <span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1042" o:ole="" style="height: 20.25pt; width: 24.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image015.wmz"></imagedata></shape></span>-----------(2)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">(1) + (2)<span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1043" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image029.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1044" o:ole="" style="height: 20.25pt; width: 24pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image013.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>+ <span style="mso-text-raise: -7.0pt; position: relative; top: 7pt;"><shape id="_x0000_i1045" o:ole="" style="height: 20.25pt; width: 24.75pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image015.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>= 40N + 384 ---------------------(3)</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">From the given statement,</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">(3) = decreasing the age of the class by 4 years</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;">40 n + 384 = (n +2) 36 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1046" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image027.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>40n – 36n = 432 – 384</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;">N = 12</b></div><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">11. One year ago, a father was four times as old as his son. In 6 years time his age exceeds twice his son’s age by 9 years. The ratio of their present ages is :</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">Answer : 11:3</span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b><br />
<div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : Let the present age of father be x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Let the present age of son be y years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1047" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image030.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>x – 1 = 4 (y – 1)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X -1 = 4y – 4</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X – 4y = -3 -----------------(1)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : In 6 years time, father age exceeds twice son by 9 years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>X + 6 = 2 (y +6) +9)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X – 2y = 21 – 6</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X – 2y = 15 ---------------(2)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">(1) – (2) <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1048" o:ole="" style="height: 11.25pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image031.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>-2y = -15</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Y = 9</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1049" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image030.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>put y = a in (1) we get x value as 33</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find: Ratio of present age of father and son</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>X : y = ?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1050" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image032.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>33 : 9 ; <b style="mso-bidi-font-weight: normal;">The ratio of present age of father and son = 11:3</b></span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">12. Ramlal is four times as old as his son. Four years hence, the sum of their ages will be 43 years. The present age of the son is :</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">Answer : 7</span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b> <br />
<div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of Ramlal be x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of son be y years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : x = 4y <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1051" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image032.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>x – 4y = 0 ---------------(1)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : x +4 + y + 4 = 43</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>X + y<span style="mso-spacerun: yes;"> </span>= 35 ------------------------ (2)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find : Present age of son (ie) y = ?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 55.5pt; mso-list: l1 level1 lfo2; tab-stops: list 55.5pt; text-align: justify; text-indent: -19.5pt;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-list: Ignore;">(1)<span style="font: 7pt "Times New Roman";"> </span></span></span><span style="font-size: 14pt; line-height: 150%;">– (2) </span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -0.25in;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-list: Ignore;">-<span style="font: 7pt "Times New Roman";"> </span></span></span><span style="font-size: 14pt; line-height: 150%;">5y = - 35</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.25in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Y = 7</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt 0.25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">Answer : Present age of son is 7 years</span></b></div></div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-68618788374189543972011-03-19T09:46:00.000-07:002011-03-19T09:46:17.691-07:00Problems on Trains<div dir="ltr" style="text-align: left;" trbidi="on"><ol><li>A train 140 m long running at 72 kmph.In how much time will it pass a platform 260m long. Total distance to cover = 140+260 = 400 time = distance / speed speed in meters per second = 72 *5/18 = 20 meters per second time = 400/20 = 20 seconds answer </li>
<li>A man is standing on a railway bridge which is 180 m.He finds that a train crosses the bridge in 20 seconds but himself in 8 sec. Find the length of the train and its sppeed Let us assume the length of train = X the speed of train = x meters/8 180 meters are covered by train in (20-8) seconds 180/12 = 15 meters per second. Thus the length of train is : 15*8 = 120 meters. Answer </li>
<li>A train 150m long is running with a speed of 54 Km per hour. In what time will it pass a man who is running at a speed of 9 km ph in the same direction in which the train is going Speed of train = 54 * 5/18 = 15 meters per second speed of mann = 9 * 5/18 = 2.5 meters per second distance to cover = 150 time = 150/(15-2.5) =12 seconds answer </li>
<li>A train 220m long is running with a speed of 59 k m ph ..In what time will it pass a man who is running at 4 kmph in the direction opposite to that in which train is going. Distance to cover = 220 meters speed = 59+4 = 63 km per hour. In meters per second = 63*5/18 = 17.5 meters per second. Time required : 220/17.5 =12.57 seconds. Answer </li>
<li>Two trains 137m and 163m in length are running towards each other on parallel lines,one at the rate of 42kmph & another at 48 mph.In wht time will they be clear of each other from the moment they meet. Distance to cover 137+163 = 300 meters speed = 42+48 = 90 km per hour speed in meters per second = 90 * 5/18 = 25 meters per second time required = 300/25 = 12 seconds answer </li>
<li>A train running at 54 kmph takes 20 sec to pass a platform. Next it takes 12 sec to pass a man walking at 6kmph in the same direction in which the train is going.Find length of the train and length of platform Solution : Train v/s man speed = 54 -6 = 48 km per hour speed in m/s =48 * 5/18 = 13.33 m / s length of train = 12*13.33 = 159.6 meters speed for platform =54*5/18 = 15 m / s length of platform+ train = 20*15 = 300 length of platform = 300 – 159 = 140 meters approx. </li>
<li>A man sitting in a train which is travelling at 50mph observes that a goods train travelling in opposite direction takes 9 sec to pass him .If the goods train is 150m long find its speed Solution : - Distance travelled = 150 speed =150/9 = 16.66 meters per second or 16.66 * 18/5 = 60 km per hour approx. Thus the speed of goods train is 60-50 = 10 km per hour. Answer </li>
<li>Two trains are moving in the same direction at 65kmph and 47kmph. The faster train crosses a man in slower train in18sec.the length of the faster train is Solution : = When the trains are going in same direction, we take difference of their speed. 65-47 =18 km per hour or 5 meters per second distance travelled =(time 18 seconds * speed 5 meters per second) = 18 * 5 = 90 meters. Thus the length of faster train is 90 meters. Answer </li>
<li>A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2kmph and 4kmph and passes them completely in 9 sec and 10 sec respectively. The length of train is Solution : - let us assume the speed of train to be X. (X-2) * 9/3600 = (X-4) *10/3600 9X – 18 = 10X – 40 X=22 km per hour. thus distance travelled = (22-4) * 5/18 = 5 m/s time=10 seconds so length of train = 5*10 = 50 meters. Answer </li>
<li>Two stations A & B are 110 km apart on a straight line. One train starts from A at 7am and travels towards B at 20kmph. Another train starts from B at 8am an travels toward A at a speed of 25kmph.At what time will they meet From 7 am to 8 am only A is travelling. It would travel 20 km. Now 90 km is to be covered. 90 / (20+25) =2 hours so at 10 am they will meet. </li>
<li>A train travelling at 48kmph completely crosses another train having half its length an travelling inopposite direction at 42kmph in12 sec.It also passes a railway platform in 45sec.the length of platform is Distance by 2 trains = (48+42) = 90 or 25 m/s 25 * 12=300 meters. So the length of train is 200 meters. Platform : 48 * 5/18 =13.33 m/ s 45*13.33 = 600 so length of platform = 600-200=400 meters. Answer </li>
<li>Find the time taken by a train 180m long,running at 72kmph in crossing an electric pole Speed of train = 72 * 5/18 = 20 m / s time required = 180/20 = 6 seconds. Answer </li>
<li>Two concentric circles form a ring. The inner and outer circumference of the ring are 352/7 m and 528/7m respectively. Find the width of the ring. Solution: Formula of circumference = 2 Pi * radius 2 * 22/7 * radius = 352/7 radius = 8 Formula of circumference = 2 Pi * radius 2 * 22/7 * radius = 528/7 radius = 12 thus width of ring = 12-8 = 4 answer </li>
<li>Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is Solution : area of one circle = (22/7) * 7 * 7 =154 square of on one circle = 14*14 = 196 difference of area : 42 one side 42/4 =10.5 we have 4 cirlces, each has 10.5 cm of space enclosed, so total space enclosed is 42 sq. cm. Answer </li>
<li>A semicircular shaped window has diameter of 63cm. Its perimeter equals Circumference of circle = diameter * 22/7 = 63 * 22/7 = 198 it is semicircle so divide by 2 = 99 add diameter also – to denote one side : 99+63 = 162 cm answer </li>
<li>The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter. Total area = 5.5 * 3.75 =20.63 multiply it by 800 =Rs.16500 </li>
<li>The no of revolutions a wheel of diameter 49 cm makes in traveling a distance of 176m is Solution : circumference = 22/7 * 49 = 154 17600 / 154 = 114.29 thus the wheel will make 115 revolutions. Answer </li>
<li>.A cow s tethered in the middle of a field with a 14feet long rope.If the cow grazes 100 sq feet per day, then approximately what time will be taken by the cow to graze the whole field? Solution Area 22/7 * 14 * 14 = 616 time required = 616/100 = 6.16 so cow will take little over 6 days to completely graze the whole field. Answer </li>
<li>A man runs round a circular field of radius 49m at the speed of 120 m/hr. What is the time taken by the man to take twenty rounds of the field? Solution : circumference = 2* 22/7 * 49 =308 total distance to be travelled = 308 * 20 = 6160 time required = 6160/120 =51.3 hours. </li>
<li>.The wheel of a motorcycle 70cm in diameter makes 40 revolutions in every 10sec. What is the speed of motorcycle in km/hr? Speed covered in 1 seconds : 4 * 22/7 *70 =880 cm or 8.8 meters. Speed in km per hour : 8.8 * 18/5 = 31.68 km per hour answer </li>
<li>A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be Solution : its circumference is : 2 * 22/7 *56 = 352 when you make a circle out of it, one side will be : 352/4 = 88 thus its area will be : 88*88 =7744 answer </li>
<li>The area of the largest triangle that can be inscribed in a semicircle of radius 2 is? Area of triangle = Formula = 1/2 * base * height = ½ * (2+2) *2 =4 answer </li>
<li>A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed? The total boundary = 2(90+50)= 280 280/5 = 56 so we will need 56 poles </li>
</ol></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-34230026110077320522011-03-15T08:53:00.000-07:002011-03-15T08:53:46.064-07:00Problems on directions<div dir="ltr" style="text-align: left;" trbidi="on">DIRECTIONS 1.Sham travels 7 km north , then turns right and walks 3 km. He again turns to <br />
his righthand side and moves 7 kn forward.how many km is sham away from the<br />
place of his starting the journey?<br />
a)7 km b)3 c)8 d)17<br />
2.Reeta drives to North of her place ofstay A and finds after travelling 25 km<br />
that she has driven in the wrong direction. she then turns to the right and<br />
travels 2 km and then again turns right and drives straigh another 25 km. how <br />
much distance she has now to cover to goback to the point from where she has <br />
started?<br />
a)25 b)2 c)5 d)68<br />
3.Rana travels 10 km north turns left and travels 4 km and then again turns right<br />
and covers another 5km. He then turns to righthand side and travels another 4 km.<br />
how far is he from the point of starting his journey?<br />
a)15 b)8 c)5 d)none<br />
4.Seeta and ram both start from a point towards north.Seeta turns to left after <br />
walking 10 km. Ram turns right after walking the same distance.seeta waits for <br />
some time and then walks another 5 km,whereas ram walks only 3 km. they both then<br />
return to their respective south and walk 15 km forward. how far is seeta from ram?<br />
a)15 b)10 C)8 d)12<br />
5.A taxi driver commenced his journey from a point and drove 10 km towards north<br />
and turned left and drove another 5 km.after waiting to meet one ofhis friends<br />
,he turned to his right and continued to drive another 10 km.He has covered a<br />
distance of 25 km so far but in which direction he now may be><br />
a)north b)east c)west d)south<br />
6.There is a ring road connecting points A,B,C and D.The road is in a complete <br />
circular form but having several approach roads leading to the centre. exactly in<br />
the centre of the ring road there is a tree which is 20 km from point A on the <br />
circular road.you have taken a round of the circular road starting from point A<br />
and finish at the same point after touching points B,C and D.you then drive 20km <br />
interior towards the tree from point A and from there reach somewhere in between<br />
B and C on the ring road. How much distance you have to travel from the tree to <br />
reach the point between B and C on the ring road?<br />
a)20 b)15 c)79 d)78<br />
7.A tourist drives 10 km towards east and turns to righthand side and takes a<br />
drive of another 3 km .he then drives towards west another 3km . he then turns<br />
to his left and walks another 2km.Afterwards, he turns right and travels 7 km.<br />
how far is he from his starting pint and in which direction?<br />
a)10km east b)8km north c)5 km west d)5km south<br />
8.Rahul walks 30 metres towards south.then turns to his right and starts walking <br />
straight till he completes another 30 meters.then again turning to his left he<br />
walks for 20 meters.he then turns to his left and walks for 30 metres.how far <br />
is he from his initial position?<br />
a)50 b)78 c)23 d)67<br />
9.Vandana drove her car for 30 km due north. then she turned left and drove for <br />
40 km,she then turned left again and drove yet another 30 km.again she turned left <br />
and drove her car 50km.how far do u think she actually drove her car from the initial<br />
position?<br />
a)10 B)5 c)89 d)none<br />
10.Shalloo ran 20 m to the east, then he turned left and walked for 15m then turned<br />
right and went 25 m and then tturned right agian and went 15m . how far was shalloo<br />
from the starting point?<br />
a)45 b)35 c)25 d)15</div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-83349818296673874632011-03-15T08:46:00.000-07:002011-03-15T08:46:24.691-07:00Problems on blood relations<div dir="ltr" style="text-align: left;" trbidi="on">Passage (questions 9 to 12):<br />
<pre></pre><pre><span> </span>Amit is the son of Rahul.Sarika,Rahul's sister has a son sonu and a daughter Rita.</pre><pre>Raja is the maternal uncle of sonu.</pre><pre></pre><pre>9. How is Amit related to sonu?</pre><pre><span> </span>a)Nephew<span> </span>b)Cousin(brother)<span> </span>c)uncle<span> </span>d)brother</pre><pre><span> </span>e)none of these</pre><pre>10. How is rita related to raja?</pre><pre><span> </span>a)sister<span> </span>b)daughter<span> </span>c)niece<span> </span>d)aunt</pre><pre><span> </span>e)none of these</pre><pre>11.How many nephews does raja have?</pre><pre><span> </span>a)1<span> </span>b)2<span> </span>c)3<span> </span>d)4<span> </span>e)none</pre><pre>12.What is the relationship of Raja with Rita?</pre><pre><span> </span>a)uncle<span> </span>b)brother<span> </span>c)maternal uncle<span> </span>d)nephew</pre><pre><span> </span>e)cant be determined</pre><pre></pre><pre>Directions:Following questions pertains to Ques 13 - 15</pre><pre></pre><pre>There are six persons S1,S2,S3,S4,S5 and S6</pre><pre>S3 is the sister of S6</pre><pre>S2 is the brother of S5's husband</pre><pre>S4 is the father of S1 and grandfather of S6.</pre><pre>There are 2 fathers, one mother and 3 brothers in the family</pre><pre></pre><pre>13. Who is S5's husband?</pre><pre><span> </span>a)S2<span> </span>b)S3<span> </span>c)S1<span> </span>d)S4<span> </span>e)S6</pre><pre>14.Who is the mother?</pre><pre><span> </span>a)S1<span> </span>b)S2<span> </span>c)S3<span> </span>d)S5<span> </span>e)cannot be determined</pre><pre>15.How many male members are there?</pre><pre><span> </span>a)1<span> </span>b)2<span> </span>c)3<span> </span>d)4<span> </span>d)cannot be determined</pre><pre></pre><pre></pre><pre>Passage (Questions 16-20)</pre><pre></pre><pre><span> </span>Mr and Mrs sharma have two children Asha and Shashi. Shashi married Radha, </pre><pre>daughter of Mrs Mahajan. Suresh , son of Mrs Mahajan married Rita. Sonu and</pre><pre>Rocky are born to Suresh and Rita. Uma and Sudha are the daughters of Shashi </pre><pre>and Radha.</pre><pre></pre><pre>16. What is Sudha's relation to Asha?</pre><pre><span> </span>a) Sister<span> </span>b)niece<span> </span>c)Aunt<span> </span>d)Daughter</pre><pre><span> </span>e)none of these</pre><pre>17.How is Sonu related to Mr Mahajan?</pre><pre><span> </span>a)son in law<span> </span>b)sib<span> </span>c)grandson<span> </span>d)none of these</pre><pre><span> </span>e)cannot be determined</pre><pre>18.How is Asha related to Radha?</pre><pre><span> </span>a)mother in law<span> </span>b)aunt<span> </span>c)sister in law<span> </span>d)niece</pre><pre><span> </span>e)none of the above</pre><pre>19.What is the surname of sonu?</pre><pre><span> </span>a)Mahajan<span> </span>b)sharma<span> </span>c)shashi<span> </span>d)cannot be detemined</pre><pre><span> </span>e)none</pre><pre>20.How is suresh related to sudha?</pre><pre><span> </span>a)brother<span> </span>b)maternal uncle<span> </span>c)uncle<span> </span>d)cousin</pre><pre><span> </span>e)cannot be determined</pre></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-87018517748463823612011-02-14T03:29:00.000-08:002011-02-14T03:29:29.224-08:00Problem on Permutation (Interesting One)<div dir="ltr" style="text-align: left;" trbidi="on"><span style="color: black; font-family: "Verdana", "sans-serif"; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><strong>Using the digits 1,5,2,8 four digit numbers are formed and the sum of all possible such numbers? </strong></span><br />
<br />
<span style="color: black; font-family: "Verdana", "sans-serif"; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><div class="MsoNormal" style="background: white; line-height: normal; margin: 0in 0in 10pt; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 3;"><b><span style="color: #003366; font-family: "Arial", "sans-serif"; font-size: 12pt; mso-fareast-font-family: "Times New Roman";">Answer</span></b></div><div class="MsoNormal" style="background: white; line-height: normal; margin: 0in 0in 7.5pt;"><span style="color: black; font-family: "Verdana", "sans-serif"; font-size: 9pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">24 numbers can be formed. 1528 1582 1258 1285 1825 1852 2158 2185 2581 2518 2851 2815 5128 5182 5218 5281 5812 5821 8152 8125 8512 8521 8215 8251.<br />
<br />
each number comes 6 times in unit 10's 100's and 1000th places.<br />
<br />
The sum is 106656</span></div><div class="MsoNormal" style="background: white; line-height: normal; margin: 0in 0in 0pt;"><span style="color: black; font-family: "Verdana", "sans-serif"; font-size: 9pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">1*6+5*6+2*6+8*6 96 </span></div><div class="MsoNormal" style="background: white; line-height: normal; margin: 0in 0in 0pt;"><br />
</div><div class="MsoNormal" style="background: white; line-height: normal; margin: 0in 0in 0pt;"><span style="color: black; font-family: "Verdana", "sans-serif"; font-size: 9pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">96+96(10)+96(100)+96(1000) 106656</span></div><div class="MsoNormal" style="background: white; line-height: normal; margin: 0in 0in 0pt;"><br />
</div></span> </div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-43724995230902294752011-02-11T08:05:00.000-08:002011-02-11T08:05:02.655-08:00Problems on Time and Work<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-family: Calibri;">1) Problem: If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day</span> <div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">can do it in how many days?</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>so (9*6*88/1) = (6*8*d/1)</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>on solving, d = 99 days.</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">2) Problem: If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">should be engaged to finish the rest of the work in 6 days working 9 hours a day?</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>so, (34*8*9/(2/5)) = (x*6*9/(3/5))</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">so x = 136 men</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>number of men to be added to finish the work = 136-34 = 102 men </span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">3) Problem: If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">do the same work?</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">Solution: Given that 5 women is equal to 8 girls to complete a work. So, 10 women = 16 girls. Therefore 10</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">women + 5 girls = 16 girls + 5 girls = 21 girls. 8 girls can do a work in 84 days then 21 girls can do a work in</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">(8*84/21) = 32 days. Therefore 10 women and 5 girls can a work in 32 days</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">4) Problem: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">take both A & B, working together but independently, to do the same job?</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">Solution: A's one hour work = 1/8. B's one hour work = 1/10. (A+B)'s one hour work = 1/8+1/10 = 9/40. Both</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">A & B can finish the work in 40/9 days</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">5) Problem: A can finish a work in 18 days and B can do the same work in half the time taken by A. Then,</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">working together, what part of the same work they can finish in a day?</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">Solution: Given that B alone can complete the same work in days = half the time taken by A = 9 days</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>A's one day work = 1/18</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>B's one day work = 1/9</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>(A+B)'s one day work = 1/18+1/9 = 1/6</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">6) Problem: A is twice as good a workman as B and together they finish a piece of work in 18 days.In how</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">many days will A alone finish the work.</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;">Solution: if A takes x days to do a work then B takes 2x days to do the same work</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>= > 1/x+1/2x = 1/18</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>= > 3/2x = 1/18</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>= > x = 27 days.</span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>Hence, A alone can finish the work in 27 days.</span></div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-5235325188754253492011-02-11T02:23:00.000-08:002011-02-11T07:53:27.156-08:00Problems on Ages with solution<div dir="ltr" style="text-align: left;" trbidi="on"><div align="center" class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: center;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 18pt; line-height: 150%;">PROBLEMS ON AGES</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">1. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><b style="mso-bidi-font-weight: normal;">a. 24<span style="mso-tab-count: 1;"> </span></b><span style="mso-tab-count: 2;"> </span>b. 27<span style="mso-tab-count: 3;"> </span>c. 40<span style="mso-tab-count: 2;"> </span>d. None of these</span></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: 0in; text-align: justify;"><rect id="_x0000_s1027" style="height: 13.7pt; left: 0px; margin-left: 405pt; margin-top: 2.4pt; position: absolute; text-align: left; width: 27pt; z-index: 251602432;"></rect><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Basic Formula:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">If the present age of A is ‘x’ years, the age of A, n years ago was (x-n) years, and the age of a after n years will be (x+n) years.<b style="mso-bidi-font-weight: normal;"></b></span></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : The ratio of the present ages of Sameer and Anand is 5:4</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present ages of Sameer be 5x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present ages of Anand be 4x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given: 3years hence (after), the ratio is 11 : 9</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">5x + 3<span style="mso-tab-count: 2;"> </span>:<span style="mso-tab-count: 1;"> </span>4x + 3</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">11<span style="mso-tab-count: 2;"> </span>:<span style="mso-tab-count: 1;"> </span>9</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><stroke joinstyle="miter"></stroke><formulas><f eqn="if lineDrawn pixelLineWidth 0"></f><f eqn="sum @0 1 0"></f><f eqn="sum 0 0 @1"></f><f eqn="prod @2 1 2"></f><f eqn="prod @3 21600 pixelWidth"></f><f eqn="prod @3 21600 pixelHeight"></f><f eqn="sum @0 0 1"></f><f eqn="prod @6 1 2"></f><f eqn="prod @7 21600 pixelWidth"></f><f eqn="sum @8 21600 0"></f><f eqn="prod @7 21600 pixelHeight"></f><f eqn="sum @10 21600 0"></f></formulas><path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"></path><lock aspectratio="t" v:ext="edit"></lock></shapetype><shape id="_x0000_i1025" o:ole="" style="height: 30.75pt; width: 35.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz"></imagedata></shape></span><span style="mso-tab-count: 2;"> </span>=<span style="mso-tab-count: 1;"> </span>11/9</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">(5x+3) 9<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>11 (4x + 3)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">45x +27 <span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>44x +33</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">45x -44x<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>33-27</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X<span style="mso-tab-count: 2;"> </span>=<span style="mso-tab-count: 1;"> </span>6</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find: Present age of Anand</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1029" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image005.wmz"></imagedata></shape></span>The present age of Anand is 4(6) years = 24 years<span style="mso-tab-count: 1;"> </span></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -27pt 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">2. The ratio of the present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>a. 1 : 4<span style="mso-tab-count: 3;"> </span>b. 2 : 3<span style="mso-tab-count: 3;"> </span><b style="mso-bidi-font-weight: normal;">c. 3 : 5<span style="mso-tab-count: 1;"> </span></b><span style="mso-tab-count: 2;"> </span>d. 5 : 6</span></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: 0in; text-align: justify;"><rect id="_x0000_s1030" style="height: 13.7pt; left: 0px; margin-left: 405pt; margin-top: 2.4pt; position: absolute; text-align: left; width: 27pt; z-index: 251605504;"></rect><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;"></span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><span style="font-size: 14pt;">Let the two brothers be X and Y</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given: The ratio of the present ages of X and Y is 1:2</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of X be x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of Y be 2x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span><b style="mso-bidi-font-weight: normal;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1026" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"> <imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image005.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span></b>X : Y<b style="mso-bidi-font-weight: normal;"></b></span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1027" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>x : 2x</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : 5 years back (before), the ratio was 1:3</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">x-5<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>1<span style="mso-tab-count: 1;"> </span>: <span style="mso-tab-count: 1;"> </span>2x-5<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>3</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1028" o:ole="" style="height: 30.75pt; width: 35.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image009.wmz"></imagedata></shape></span><span style="mso-tab-count: 2;"> </span>=<span style="mso-tab-count: 1;"> </span>1/3</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">3 (x-5)<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>2x-5</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">3x-15 <span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>2x-5 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1030" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>3x-2x<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>-5 +15 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1031" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>x = 10</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find : The ratio of their ages after 5 years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">X+5<span style="mso-tab-count: 1;"> </span>= ?<span style="mso-tab-count: 1;"> </span>: <span style="mso-tab-count: 1;"> </span>2x + 5 =<span style="mso-tab-count: 1;"> </span>?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">10 + 5 = 15<span style="mso-tab-count: 1;"> </span>:<span style="mso-tab-count: 1;"> </span>2(10)+5 = 25</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1032" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>15 : 25<span style="mso-tab-count: 1;"> </span><b style="mso-bidi-font-weight: normal;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1033" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>3 : 5</b></span></div><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="page-break-before: always;" /></span><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">3. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span>a. 8, 20, 28<span style="mso-tab-count: 2;"> </span><b style="mso-bidi-font-weight: normal;">b. 16, 28, 36</b><span style="mso-tab-count: 2;"> </span>c. 20, 35, 45<span style="mso-tab-count: 2;"> </span>d. None of these</span></div><div class="MsoNormal" style="margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: 0in; text-align: justify;"><rect id="_x0000_s1033" style="height: 13.7pt; left: 0px; margin-left: 405pt; margin-top: 2.4pt; position: absolute; text-align: left; width: 27pt; z-index: 251608576;"></rect><rect id="_x0000_s1034" style="height: 13.7pt; left: 0px; margin-left: 4in; margin-top: 2.4pt; position: absolute; text-align: left; width: 27pt; z-index: 251609600;"></rect><rect id="_x0000_s1032" style="height: 13.7pt; left: 0px; margin-left: 2in; margin-top: 2.65pt; position: absolute; text-align: left; width: 27pt; z-index: 251607552;"></rect></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the 3 persons be A, B and C</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : The ratio of the present ages of 3 persons is 4:7:9</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of A be 4x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of B be 7x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Let the present age of C be 9x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">A : B : C <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1034" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>4x : 7x : 9x</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : 8 years ago, the sum of their ages was 56.</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 2;"> </span>8 years ago, the ratio of the ages is </span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">A : B : C <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1035" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>4x – 8 : 7x – 8 : 9x – 8</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : The sum of the above ages was 56</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 2;"> </span>4x -8 + 7x-8 + 9x-8<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>56</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 2;"> </span>20x – 24 = 56 <span style="mso-tab-count: 1;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1036" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>20x = 56+24<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1037" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>20x=80</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 3;"> </span>x<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>4</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">To find : A, B and C’s present age.</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span>A : B : C</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">4x : 7x : 9x <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1049" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>4 (4) : 7 (4) : 9 (4)</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2pt;"><shape id="_x0000_i1038" o:ole="" style="height: 9.75pt; width: 11.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image005.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>A’s Age = 16 ; B’s Age = 28 ; C’s Age = 36</span></b><span style="font-size: 14pt; line-height: 150%;"></span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span>4. The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A’s age 4 years ago and B’s age 4 years hence is 1 : 1. What is the ratio between A’s age 4 years hence and B’s age 4 years ago?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>a. 1 : 3<span style="mso-tab-count: 3;"> </span>b. 2 : 1<span style="mso-tab-count: 3;"> </span><b style="mso-bidi-font-weight: normal;">c. 3 : 1<span style="mso-tab-count: 1;"> </span></b><span style="mso-tab-count: 2;"> </span>d. 4 : </span></div><div class="MsoNormal" style="margin: 0in 0in 0pt; tab-stops: list .25in; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Answer with Explanation:</span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : The ratio between the present ages of A and B is 5 : 3</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Let the present age of A is 5x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>Let the present age of B is 3x years</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in -0.5in 0pt 0in; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">Given : The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">A’s age 4 years ago = 5x - 4</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">B’s age 4 years hence<span style="mso-tab-count: 1;"> </span>= 3x + 4<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span></span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">5x-4<span style="mso-tab-count: 1;"> </span>= 1 ; 3x +4<span style="mso-spacerun: yes;"> </span>= 1</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;"><span style="mso-text-raise: -12.0pt; position: relative; top: 12pt;"><shape id="_x0000_i1050" o:ole="" style="height: 30.75pt; width: 35.25pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image011.wmz"></imagedata></shape></span><span style="mso-tab-count: 2;"> </span>=<span style="mso-tab-count: 1;"> </span>1/1</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">5x-4<span style="mso-tab-count: 1;"> </span>= 3x +4 <span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1051" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>5x – 3x <span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>4 + 4 <span style="mso-tab-count: 1;"></span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1052" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>2x =8 <span style="mso-tab-count: 1;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1053" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span>x = 4</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; line-height: 150%;">To find : </span></b></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">5x+4<span style="mso-tab-count: 1;"> </span>= ?<span style="mso-tab-count: 1;"> </span>:<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>3x - 4<span style="mso-spacerun: yes;"> </span>= ?</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">20 + 4 <span style="mso-tab-count: 1;"> </span>= <span style="mso-tab-count: 1;"> </span>24 : 12 – 4</span></div><div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><span style="font-size: 14pt; line-height: 150%;">24 : 8<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-text-raise: -3.0pt; position: relative; top: 3pt;"><shape id="_x0000_i1039" o:ole="" style="height: 12pt; width: 15pt;" type="#_x0000_t75"><imagedata o:title="" src="file:///C:\Users\om\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz"></imagedata></shape></span><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><b style="mso-bidi-font-weight: normal;">3 : 1</b></span></div><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify; text-indent: 0.5in;"><br />
</div><br />
<div class="MsoNormal" style="line-height: 150%; margin: 0in 0in 0pt; text-align: justify;"><sub><span style="font-size: 14pt; line-height: 150%;"><span style="color: red;">FOR MORE PROBLEMS</span> <a href="http://www.aptitudecoach.com/apt_qs/Problems%20on%20Ages.37.doc">CLICK HERE</a></span></sub></div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-66380715152086640802011-02-06T01:33:00.000-08:002011-02-06T01:33:19.183-08:00Important Concepts on Permutation<div dir="ltr" style="text-align: left;" trbidi="on"><div class="MsoNormal"><span style="color: red; font-family: Arial; font-size: large;"><strong>Permutation</strong></span></div><div class="MsoNormal"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; mso-list: l2 level1 lfo1; tab-stops: list .75in; text-indent: -0.5in;"><span style="color: #0000a0; font-family: Arial;">Number of permutations of ‘n’ different things taken ‘r’ at a time is given by:-</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;"><span style="color: #0000a0; font-family: Arial;"><sup>n</sup>P<sub>r</sub> = n!/(n-r)!</span></div><div class="MsoNormal" style="margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;"><strong>Proof</strong>: Say we have ‘n’ different things a<sub>1</sub>, a<sub>2</sub>……, a<sub>n</sub>.</span></div><div class="MsoNormal" style="margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Clearly the first place can be filled up in ‘n’ ways. Number of things left after filling-up the first place = n-1</span></div><div class="MsoNormal" style="margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">So the second-place can be filled-up in (n-1) ways. Now number of things left after filling-up the first and second places = n - 2</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Now the third place can be filled-up in (n-2) ways.</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Thus number of ways of filling-up first-place = n</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up second-place = n-1</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up third-place = n-2</span></div><div class="MsoNormal" style="margin-left: 0.5in; tab-stops: .5in; text-indent: -0.5in;"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up r-th place = n – (r-1) = n-r+1</span></div><div class="MsoNormal" style="margin-left: 0.5in; tab-stops: .5in; text-indent: -0.5in;"><span style="color: #800040; font-family: Arial;">By multiplication – rule of counting, total no. of ways of filling up, first, second -- rth-place together :-</span></div><div class="MsoNormal"><span style="color: #800040; font-family: Arial;">n (n-1) (n-2) ------------ (n-r+1)</span></div><div class="MsoNormal" style="text-indent: 0.5in;"><span style="color: #800040; font-family: Arial;">Hence:<br />
<sup>n</sup>P<sub>r</sub> = n (n-1)(n-2) --------------(n-r+1)</span></div><div class="MsoNormal" style="line-height: 150%;"><span style="color: #800040; font-family: Arial;">= [n(n-1)(n-2)----------(n-r+1)] [(n-r)(n-r-1)-----3.2.1.] / [(n-r)(n-r-1)] ----3.2.1</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;"><span style="color: #800040; font-family: Arial;"><sup>n</sup>P<sub>r</sub> = n!/(n-r)!</span></div><div class="MsoNormal" style="margin-left: 0.75in; mso-list: l5 level1 lfo2; tab-stops: list .75in; text-indent: -0.5in;"><span style="color: #800040; font-family: Arial;">Number of permutations of ‘n’ different things taken all at a time is given by:-</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-indent: 0.25in;"><span style="color: #800040; font-family: Arial;"><sup>n</sup>P<sub>n</sub> = n!</span></div><div class="MsoNormal"><span style="color: #800040; font-family: Arial;">Proof : <br />
Now we have ‘n’ objects, and n-places.</span></div><div class="MsoNormal"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up first-place = n</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up second-place = n-1</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; tab-stops: 45.0pt; text-indent: -45pt;"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up third-place = n-2</span></div><div class="MsoNormal" style="margin-left: 0.5in; tab-stops: .5in; text-indent: -0.5in;"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up r-th place, i.e. last place =1</span></div><div class="MsoNormal"><span style="color: #800040; font-family: Arial;">Number of ways of filling-up first, second, --- n th place<br />
= n (n-1) (n-2) ------ 2.1.</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;"><span style="color: #800040; font-family: Arial;"><sup>n</sup>P<sub>n</sub> = n!</span></div><div class="MsoNormal" style="line-height: 150%;"><span style="color: #0000a0; font-family: Arial;">Concept. </span></div><div class="MsoNormal" style="line-height: 150%;"><span style="color: #0000a0; font-family: Arial;">We have <sup>n</sup>P<sub>r</sub> = n!/n-r</span></div><div class="MsoNormal"><span style="color: #0000a0; font-family: Arial;">Putting r = n, we have :-</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;"><span style="color: #0000a0; font-family: Arial;"><sup>n</sup>P<sub>r</sub> = n! / (n-r)</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;"><span style="color: #0000a0; font-family: Arial;">But <sup>n</sup>P<sub>n </sub>= n!</span></div><div class="MsoNormal"><span style="color: #0000a0; font-family: Arial;">Clearly it is possible, only when n! = 1</span></div><div class="MsoNormal"><span style="color: #0000a0; font-family: Arial;">Hence it is proof that 0! = 1</span></div><div class="MsoNormal"><br />
</div><div class="MsoNormal"><span style="color: #0000a0; font-family: Arial;"><span style="font-size: large;"><strong>Note</strong> : Factorial of negative-number is not defined. The expression –3! has no meaning.</span></span></div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-38198236434216776222011-02-03T23:05:00.000-08:002011-02-03T23:05:18.144-08:00Important formula for Boats and Streams<div dir="ltr" style="text-align: left;" trbidi="on"><strong><span style="font-size: large;"> BOATS AND STREAMS</span></strong><br />
<br />
<div class="layer scale_hack" style="z-index: 4;"><div class="middle_layer"><div class="inner_layer" style="font-size: 0.1em;"><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 15.7em; word-spacing: 0.05em;"><strong>1.In water ,the direction along the stream is called downstream and ,the direction against </strong></div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 16.96em; word-spacing: 0.01em;"><strong>the stream is called upstream. </strong></div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 19.49em; word-spacing: 0.26em;"><strong></strong> </div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 19.49em; word-spacing: 0.26em;"><strong>2.If the speed of a boat in still water is u km/hr and the speed of the stream is v </strong></div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 20.75em;"><strong>km/hr,then: </strong></div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 20.75em;"><strong></strong> </div><div class="ff0" style="font-size: 9.88em; left: 12.04em; top: 22.44em;"><strong>speed downstream=(u+v)km/hr. </strong></div><div class="ff0" style="font-size: 9.88em; left: 12.04em; top: 23.71em; word-spacing: 0.01em;"><strong>speed upstream=(u-v)km/hr<span class="ff1" style="font-size: 1.02em;"><span style="font-family: cd9800318d998e9e0d5d9168#540f00;">.</span></span> </strong></div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 25.81em; word-spacing: 0.01em;"><strong></strong> </div><div class="ff1" style="font-size: 10.06em; left: 8.25em; top: 25.81em; word-spacing: 0.01em;"><strong>3.If the speed downstream is a km/hr and the speed upstream is b km/hr,then : </strong></div><div class="ff0" style="font-size: 9.88em; left: 8.4em; top: 27.59em; word-spacing: 0.01em;"><strong></strong> </div><div class="ff0" style="font-size: 9.88em; left: 8.4em; top: 27.59em; word-spacing: 0.01em;"><strong>speed in still water=1/2(a+b)km/hr </strong></div><div class="ff0" style="font-size: 9.88em; left: 8.4em; top: 28.88em;"><strong></strong> </div><div class="ff0" style="font-size: 9.88em; left: 8.4em; top: 28.88em;"><strong>rate of stream=1/2(a-b)km/hr </strong></div></div></div></div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-13123947590671223542011-02-01T05:41:00.000-08:002011-02-01T05:41:11.343-08:00<div dir="ltr" style="text-align: left;" trbidi="on"><strong>Karnataka Post Graduate Common Entrance Test 2010 Application Form was Available at</strong><br />
<br />
The Karnataka PGCET 2010 application can be obtained on payment of Rs. 600/- (Rs 300/- in case of Karnataka SC/ ST and Cat-I, on production of documentary proof) in the form of DD only, drawn in favour of the Member Secretary, CPAC payable at Belgaum.<br />
a) Karnataka PGCET 2010 Application can be obtained only in person from :<br />
1) Gulbarga University,<br />
Department of Management,<br />
“Jnana Ganga”,<br />
Gulbarga – 585106<br />
Phone No : 08472-263283.<br />
2) University of Mysore,<br />
B.N. Bahadur Institute of Management Sciences,<br />
“Manasagangothri,” MYSORE – 570 006<br />
Phone No : 0821-2413920/2419755<br />
3) Karnataka University,<br />
Kousali Institute of Management Studies,<br />
Dharwad – 580 003<br />
Phone No : 0836-2741882<br />
4) Karnataka State Women’s University,<br />
Department of PG Studies & Research in Management,<br />
Bijapur – 586 101<br />
Phone No : 08352-277503<br />
5) J N N College of Engineering,<br />
Dept. of MBA, Savalanga Road, Navule,<br />
Shimoga – 577 204<br />
Phone No : 08182-276568<br />
6) Srinivasa Institute of Technology,<br />
Merlapadavu, Arkula, P.O. Parangipet, Valachil,<br />
Mangalore – 574 143<br />
Phone No : 0824-2274730/32<br />
7) Bapuji Institute of Engineering and Technology,<br />
Shamanur Road, Davanagere – 577 004<br />
Phone No : 08192-222245<br />
8 ) Rao Bahadur Y Mahabaleshwarappa Engineering College,<br />
Cantonment, Bellary-583104,<br />
Phone No : 08392-244809<br />
9) Sahyadri Institute of Technology & Management,<br />
NH – 48, Adyar,<br />
Mangalore – 575009,<br />
Phone No : 0824 – 2277222.<br />
<br />
<strong>b) Karnataka PGCET 2010 Application can be procured in person & also by Post from :</strong><br />
<br />
1) Visvesvaraya Technological University,<br />
PGCET Cell,<br />
“Jnana Sangama”, BELGAUM – 590 018,<br />
2) VTU Regional Office,<br />
No. 351, II cross, I Block,<br />
Jayanagar, Bangalore – 560 011<br />
3) VTU Regional Office,<br />
Sri Jayachamarajendra College of Engineering Campus,<br />
Mysore – 570 006<br />
4) VTU Regional Office,<br />
Rajapura Kusnoor Road,<br />
Gulbarga – 585 106.<br />
The application can be obtained through post by applying on a plain paper indicating Name of the candidate & complete postal address, name of course for which admission is sought and enclose the DD (mention DD No., Date and Bank name) for application fee.<br />
Karnataka PGCET 2010 Important Dates :<br />
1) Last date for issue of Karnataka PGVET 2010 application form : 10-6-2010<br />
2) Completed application forms addressed must reach on or before 10-6-2010 only to,<br />
The Member Secretary CPAC, & Registrar,<br />
VTU, Jnana Sangama, Belgaum – 590 018<br />
3) The list of colleges along with Seat Matrix will be notified in the website <a href="http://www.vtu.ac.in/">http://www.vtu.ac.in/</a> & http ://pgcet.vtu.ac.in on approval of the Seat Matrix by the Government.<br />
Contact Nos : 0831-2498126/127/129..<br />
</div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com0tag:blogger.com,1999:blog-8173732925527753737.post-3379336519693072502011-01-28T19:23:00.000-08:002011-01-30T03:05:05.441-08:00Universities under PGCET<div dir="ltr" style="text-align: left;" trbidi="on"><div dir="ltr" style="text-align: left;" trbidi="on"><b><span class="Apple-style-span" style="color: orange;">Universities under PgCET are as follows</span></b><br />
<b><br />
</b><br />
<b>Bangalore University</b><br />
<b>Visveswaraya Technological University</b><br />
<b>Mysore University</b><br />
<b>Dharwad University</b><br />
<b>Tumkur University</b><br />
<b>Kuvempu University </b></div><script src="http://connect.facebook.net/en_US/all.js#xfbml=1">
</script><br />
<like></like></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com1tag:blogger.com,1999:blog-8173732925527753737.post-40556377480510203782011-01-21T07:58:00.000-08:002011-01-22T04:14:43.990-08:00Sections in PgCET(MBA)<div dir="ltr" style="text-align: left;" trbidi="on"><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style="font-family: Arial;"><strong>PGCET is for 100 marks. </strong></span></div><div style=" border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><strong><span style=""><span style=""><span style="font-family: Arial;">There will be </span><span style="font-family: Arial;">usually 100 Questions carrying one mark each.</span></span></span></strong></div><div style=" border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style=" font-family: Arial;"><strong>There are four sections of 25 questions each. </strong></span></div><ul style="text-align: left;"><li><div style=" border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style=" font-family: Arial;"><strong>Quantitative Aptitude.</strong></span></div></li>
<li><div style=" border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style=" font-family: Arial;"><strong>Logical Reasoning. </strong></span></div></li>
<li><div style=" border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style=" font-family: Arial;"><strong>Objective English.</strong></span></div></li>
<li><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style=" font-family: Arial;"><strong>General Knowledge.</strong></span></div></li>
</ul><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><strong><span><span><span style="font-family: Arial;">Four</span><span style="font-family: Arial;"> sections have equal weightage. </span></span></span></strong></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span><strong></strong></span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;overflow: hidden; text-align: left; text-decoration: none;"><span font-family: Arial;"><strong>Start Preparing for General Knowledge.</strong></span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; overflow: hidden; text-align: left; text-decoration: none;"><span style=""><strong></strong></span></div></div>Administratorhttp://www.blogger.com/profile/08679226857281577510noreply@blogger.com8