Wednesday, March 30, 2011

Number Word Problems

Number Word Problems
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.
  • The sum of two consecutive integers is 15. Find the numbers.
    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 –3 or 6), not messy ones (like –4.628 or 17/32), 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 –12 and –11, 1 and 2, and 99 and 100. Using these facts, I can set up the translation. I will represent the first number by "n". Then the second number has to be "n + 1". Their sum is then:
      n + (n + 1) = 15 2n + 1 = 15 2n = 14 n = 7   Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved
    The exercise did not ask me for the value of the variable n; it asked for the identity of two numbers. So my answer is not "n = 7"; the actual answer is:
      "The numbers are 7 and 8."
  • The product of two consecutive negative even integers is 24. Find the numbers.
    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, –4 and –2 or 10 and 12), 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 24. In other words, letting the first number be "n" and the second number be "n + 2", I have:
      (n)(n + 2) = 24 n2 + 2n = 24 n2 + 2n – 24 = 0 (n + 6)(n – 4) = 0
    Then the solutions are n = –6 and n = 4. Since the numbers I am looking for are negative, I can ignore the "4" and take n = –6. Then the next number is n + 2 = –4, and the answer is
      The numbers are –6 and –4.
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 always work, and it's sure to annoy your teacher. Throw out invalid results, and solve properly for valid ones.
  • 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 71. What are the numbers?
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:
      the larger number:  x the smaller number:  y twice the larger:  2x three more than five times the smaller:  5y + 3 relationship between ("is"):  2x = 5y + 3 four times the larger:  4x three times the smaller:  3y relationship between ("sum of"):  4x + 3y = 71
    Now I have two equations in two variables:
      2x = 5y + 3 4x + 3y = 71
    I will solve, say, the first equation for x:
      x = (5/2)y + (3/2)
    Then I'll plug the right-hand side of this into the second equation in place of the "x":
      4[ (5/2)y + (3/2) ] + 3y = 71 10y + 6 + 3y = 71 13y + 6 = 71 13y = 65 y = 65/13 = 5
    Now that I have the value for y, I can solve for x:
      x = (5/2)y + (3/2) x = (5/2)(5) + (3/2) x = (25/2) + (3/2) x = 28/2 = 14
    As always, I need to remember to answer the question that was actually asked. The solution here is not "x = 14", but is the following sentence:
      The larger number is 14, and the smaller number is 5.
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.

Saturday, March 26, 2011

Types of Prepositions with example

What are the different types of Preposition?

Preposition of place
Preposition of time
Preposition of movement

Preposition of place - at, on, in, below, beside, under, behind, between
Prepositions of place are used to describe the place or position of nouns.

Example
1.The dog is in the garden.
2.The box is behind the door
3. He threw the ball over the roof
4. She lives near the school.
5. The house is between 3rd Street and 4th Street.
6. London is on the river Thames.

Preposition of time-at, on, in, during,
Prepositions of time- used to show when something happened.

More examples: since, for, by, from -to, from-until, during, in.
1. I haven’t seen her since yesterday.
2. I'm leaving to Chennai in a week.
4. I waited for him from 8 a.m. until 10 a.m., and later went out
5. I watch TV during the evening.

Preposition of Movement
Preposition of Movement is used to show movement.

Example: to, towards, through, across, over, into, onto
To: signifies movement toward a specific destination.
Example: He went to the park.
Towards: suggests movement in a general direction,
Example: The helicopter flew towards south.
Into: Suji fell into the well.
Onto: Clara jumped onto the bench.

Articles usage in english

A, An or The?

When do we say "the dog" and when do we say "a dog"? (On this page we talk only about singular, countable nouns.)
The and a/an are called "articles". We divide them into "definite" and "indefinite" like this:

Articles
DefiniteIndefinite
thea, an

We use "definite" to mean sure, certain. "Definite" is particular.
We use "indefinite" to mean not sure, not certain. "Indefinite" is general.
When we are talking about one thing in particular, we use the. When we are talking about one thing in general, we use a or an.
Think of the sky at night. In the sky we see 1 moon and millions of stars. So normally we would say:
  • I saw the moon last night.
  • I saw a star last night.
Look at these examples:

thea, an
  • The capital of France is Paris.
  • I have found the book that I lost.
  • Have you cleaned the car?
  • There are six eggs in the fridge.
  • Please switch off the TV when you finish.
  • I was born in a town.
  • John had an omelette for lunch.
  • James Bond ordered a drink.
  • We want to buy an umbrella.
  • Have you got a pen?

Of course, often we can use the or a/an for the same word. It depends on the situation, not the word. Look at these examples:
  • We want to buy an umbrella. (Any umbrella, not a particular umbrella.)
  • Where is the umbrella? (We already have an umbrella. We are looking for our umbrella, a particular umbrella.)
This little story should help you understand the difference between the and a, an:

A man and a woman were walking in Oxford Street. The woman saw a dress that she liked in a shop. She asked the man if he could buy the dress for her. He said: "Do you think the shop will accept a cheque? I don't have a credit card."

Monday, March 21, 2011

Number series

  1.Prime Number Series

           Example:
                            2,3,5,7,11,..............

2.Even Number Series
           Example:
                             2,4,6,8,10,12,...........

3.Odd Number Series:

            Example:
                              1,3,5,7,9,11,...........
4.Perfect Squares:

             Example:
1,4,9,16,25,............

5.Perfect Cubes:

             Example:
                              1,8,27,64,125,.................

.Multiples of Number Series: 

             Example:

           3,6,9,12,15,..............are multiples of 3

7.Numbers in Arthimetic Progression(A.P):

               Example:
                                 13,11,9,7................

8.Numbers in G.P:
               Example:

                                 48,12,3,.....

Problems On Ages

Problems On Ages     
           
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 ?
Sol: Let their present ages be 4x & 6x
       Then (4x + 12)/(5x + 12) = 5/6   or x=12
        Sona's age after 6 years = (5x +6) = 66 years
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 ?
 
Sol : Let son's age 8 years ago be x years
        Then Ramu's age at that time = 4x years
         Son's age after 8 years         = (x +8) + 8  = (x + 16) years
         Ramu's age after 8 years      = (4x + 8) + 8 = (4x + 16) years
          2(x + 16) = 4x + 16   or x=8
          Son's present age = (x + 8) = 16 years
         Ramu's present age= (4x + 8) = 40 years
 
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 ?
 
Sol : Let son's age = x, then man's age =4x.
        9(x - 5) = (4x-5) or x=8.
        Man's present age = (4x + 7) = 35 years
 
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.
 
Sol : Let Aruna's age 7 years ago be x.
        Mother's age 7 years ago = 4x
        (x + 7) + (4x + 7) =49   or x=7
        Mother's present age = (4x + 7) = 35 years
 
 
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.
 
Sol : Let A's age = x   & B's age = (x + 16)
        3(x - 6) = (x + 16 - 6)   or x=14
        A's age = 14 years & B's age = 30 years.


6. 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:
            a. 5 : 2                         b. 7 : 3                         c. 9 : 2                         d. 13 : 4
Answer with Explanation:
Let the  father age be x years
Let the son’s age be y years
Given : 10 years ago, father age was thrice son age
            X – 10 = 3 (y – 10)
            x- 3y = -30 +10
            x-3y = - 20 ---------------- (1)
Given : 10 years after, father age was twice son age
X + 10 = 2 (y + 10)
X – 2y = 10 -----------------(2)
To find : Ratio of present age (x : y = ?)
To get y value subtract (2) from (1)
Y = 30 ; substitute this value in (1) we will get x value
X = 70
70 : 30
7 : 3



7. 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?
            a. 31                            b. 36                            c. 51                            d. None of these

Answer with Explanation:

36  = 14
37 = 15 (teacher’s age included then average increased  by one  ; ie =15)
To find :
Teacher’s age:
(37 – 36) 15 = (15-14) (36)
15 + 36
51 years


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?
Answer : 60
Answer with Explanation:

Let the present age of Gulzar be x years
Let the present age of Anup be y years
Let the present age of  Mahesh be z years
Given:  = y
X – 6 = 18y
X – 18y = 6
Given : Anup is 2 years younger to Mahesh
          Y = z – 2
Given : Mahesh age is 5 years
          Z = 5
 y = 5 - 2 ; y = 3
 x – 18 (3) = 6 ; X – 54 = 6 ; X = 6 + 54
X = 60
To find : Present age of gulzar
X  =  60 years


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 :
Answer : 75

Answer with Explanation:

Given :
          Number of members                         Average
                   5                                              21
                   5 +1                                         21 + 9                  
          5    21
          6   30
To find : Grand father’s age
          Grand father age = (6-5) (30) + (30-21) (5)
                                      =       30 + 45
                                      =       75



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:
Answer : 12
Mean =

Answer with Explanation:

Let  be the sum of the ages of n adults
Let  be the sum of the ages of 12 students
Given :  = 
40 =
40 n =  --------------------(1)
 =
32 =
32 x 12 =    384 = -----------(2)
(1) + (2)     +  = 40N + 384 ---------------------(3)
From the given statement,
(3) = decreasing the age of the class by 4 years
40 n + 384 = (n +2) 36  40n – 36n = 432 – 384
N = 12


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 :
Answer : 11:3


Answer with Explanation:
Given : Let the present age of father be x years
          Let the present age of son be y years
 x – 1 = 4 (y – 1)
X -1 = 4y – 4
X – 4y = -3 -----------------(1)
Given : In 6 years time, father age exceeds twice son by 9 years
          X + 6 = 2 (y +6) +9)
X – 2y = 21 – 6
X – 2y = 15 ---------------(2)
(1) – (2)  -2y = -15
Y = 9
 put y = a in (1) we get x value as 33
To find: Ratio of present age of father and son
          X : y = ?
           33 : 9 ; The ratio of present age of father and son = 11:3



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 :
Answer : 7

Answer with Explanation:

Let the present age of Ramlal be x years
Let the present age of son be y years
Given : x = 4y  x – 4y = 0 ---------------(1)
Given : x +4 + y + 4 = 43
          X + y  = 35 ------------------------ (2)
To find : Present age of son (ie) y = ?
(1)  – (2)
-         5y = - 35
Y = 7
Answer : Present age of son is 7 years

Saturday, March 19, 2011

Problems on Trains

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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.
  7. 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
  8. 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
  9. 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
  10. 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.
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. .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
  19. 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.
  20. .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
  21. 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
  22. 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
  23. 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

Tuesday, March 15, 2011

Problems on directions

DIRECTIONS 1.Sham travels 7 km north , then turns right and walks 3 km. He again turns to
his righthand side and moves 7 kn forward.how many km is sham away from the
place of his starting the journey?
a)7 km b)3 c)8 d)17
2.Reeta drives to North of her place ofstay A and finds after travelling 25 km
that she has driven in the wrong direction. she then turns to the right and
travels 2 km and then again turns right and drives straigh another 25 km. how
much distance she has now to cover to goback to the point from where she has
started?
a)25 b)2 c)5 d)68
3.Rana travels 10 km north turns left and travels 4 km and then again turns right
and covers another 5km. He then turns to righthand side and travels another 4 km.
how far is he from the point of starting his journey?
a)15 b)8 c)5 d)none
4.Seeta and ram both start from a point towards north.Seeta turns to left after
walking 10 km. Ram turns right after walking the same distance.seeta waits for
some time and then walks another 5 km,whereas ram walks only 3 km. they both then
return to their respective south and walk 15 km forward. how far is seeta from ram?
a)15 b)10 C)8 d)12
5.A taxi driver commenced his journey from a point and drove 10 km towards north
and turned left and drove another 5 km.after waiting to meet one ofhis friends
,he turned to his right and continued to drive another 10 km.He has covered a
distance of 25 km so far but in which direction he now may be>
a)north b)east c)west d)south
6.There is a ring road connecting points A,B,C and D.The road is in a complete
circular form but having several approach roads leading to the centre. exactly in
the centre of the ring road there is a tree which is 20 km from point A on the
circular road.you have taken a round of the circular road starting from point A
and finish at the same point after touching points B,C and D.you then drive 20km
interior towards the tree from point A and from there reach somewhere in between
B and C on the ring road. How much distance you have to travel from the tree to
reach the point between B and C on the ring road?
a)20 b)15 c)79 d)78
7.A tourist drives 10 km towards east and turns to righthand side and takes a
drive of another 3 km .he then drives towards west another 3km . he then turns
to his left and walks another 2km.Afterwards, he turns right and travels 7 km.
how far is he from his starting pint and in which direction?
a)10km east b)8km north c)5 km west d)5km south
8.Rahul walks 30 metres towards south.then turns to his right and starts walking
straight till he completes another 30 meters.then again turning to his left he
walks for 20 meters.he then turns to his left and walks for 30 metres.how far
is he from his initial position?
a)50 b)78 c)23 d)67
9.Vandana drove her car for 30 km due north. then she turned left and drove for
40 km,she then turned left again and drove yet another 30 km.again she turned left
and drove her car 50km.how far do u think she actually drove her car from the initial
position?
a)10 B)5 c)89 d)none
10.Shalloo ran 20 m to the east, then he turned left and walked for 15m then turned
right and went 25 m and then tturned right agian and went 15m . how far was shalloo
from the starting point?
a)45 b)35 c)25 d)15

Problems on blood relations

Passage (questions 9 to 12):
   Amit is the son of Rahul.Sarika,Rahul's sister has a son sonu and a daughter Rita.
Raja is the maternal uncle of sonu.
9. How is Amit related to sonu?
  a)Nephew     b)Cousin(brother)      c)uncle        d)brother
  e)none of these
10. How is rita related to raja?
  a)sister     b)daughter     c)niece        d)aunt
  e)none of these
11.How many nephews does raja have?
  a)1   b)2     c)3     d)4     e)none
12.What is the relationship of Raja with Rita?
  a)uncle      b)brother      c)maternal uncle       d)nephew
  e)cant be determined
Directions:Following questions pertains to Ques 13 - 15
There are six persons S1,S2,S3,S4,S5 and S6
S3 is the sister of S6
S2 is the brother of S5's husband
S4 is the father of S1 and grandfather of S6.
There are 2 fathers, one mother and 3 brothers in the family
13. Who is S5's husband?
  a)S2  b)S3    c)S1    d)S4    e)S6
14.Who is the mother?
  a)S1  b)S2    c)S3    d)S5    e)cannot be determined
15.How many male members are there?
  a)1   b)2     c)3     d)4     d)cannot be determined
Passage (Questions 16-20)
   Mr and Mrs sharma have two children Asha and Shashi. Shashi married Radha, 
daughter of Mrs Mahajan. Suresh , son of Mrs Mahajan married Rita. Sonu and
Rocky are born to Suresh and Rita. Uma and Sudha are the daughters of Shashi 
and Radha.
16. What is Sudha's relation to Asha?
  a) Sister    b)niece        c)Aunt         d)Daughter
  e)none of these
17.How is Sonu related to Mr Mahajan?
  a)son in law b)sib          c)grandson     d)none of these
  e)cannot be determined
18.How is Asha related to Radha?
  a)mother in law      b)aunt  c)sister in law d)niece
  e)none of the above
19.What is the surname of sonu?
  a)Mahajan    b)sharma       c)shashi       d)cannot be detemined
  e)none
20.How is suresh related to sudha?
  a)brother    b)maternal uncle       c)uncle d)cousin
  e)cannot be determined