Problems on Ages with solution

PROBLEMS ON AGES

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?

          a. 24                     b. 27                     c. 40            d. None of these

Basic Formula:

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.

Answer with Explanation:

Given : The ratio of the present ages of Sameer and Anand is 5:4

Let the present ages of Sameer be 5x years

Let the present ages of Anand be 4x years

Given: 3years hence (after), the ratio is 11 : 9

5x + 3                   :         4x + 3

11               :         9

                   =       11/9

(5x+3) 9      =       11 (4x + 3)

45x +27      =       44x +33

45x -44x     =       33-27

X                =       6

To find: Present age of Anand

The present age of Anand is 4(6) years = 24 years  

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?

          a. 1 : 4                            b. 2 : 3                           c. 3 : 5                       d. 5 : 6

Answer with Explanation:

Let the two brothers be X and Y

Given: The ratio of the present ages of X and Y is 1:2

Let the present age of X be x years

Let the present age of Y be 2x years

   X : Y

 x : 2x

Given : 5 years back (before), the ratio was 1:3

x-5    =       1        :         2x-5  =       3

                   =       1/3

3 (x-5)         =       2x-5

3x-15          =       2x-5  3x-2x      =       -5 +15  x = 10

To find : The ratio of their ages after 5 years

X+5   = ?     :         2x + 5 =      ?

10 + 5 = 15 :         2(10)+5 = 25

 15 : 25    3 : 5

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).

 a. 8, 20, 28          b. 16, 28, 36                  c. 20, 35, 45                   d. None of these

Answer with Explanation:

Let the 3 persons be A, B and C

Given : The ratio of the present ages of 3 persons is 4:7:9

Let the present age of A be 4x years

Let the present age of B be 7x years

Let the present age of C be 9x years

A : B : C  4x : 7x : 9x

Given : 8 years ago, the sum of their ages was 56.

                   8 years ago, the ratio of the ages is

A : B : C  4x – 8 : 7x – 8 : 9x – 8

Given : The sum of the above ages was 56

                   4x -8 + 7x-8 + 9x-8       =       56

                   20x – 24 = 56        20x = 56+24              20x=80

                             x        =       4

To find : A, B and C’s present age.

 A : B : C

4x : 7x : 9x  4 (4) : 7 (4) : 9 (4)

 A’s Age = 16 ; B’s Age = 28 ; C’s Age = 36

 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?

          a. 1 : 3                            b. 2 : 1                           c. 3 : 1                           d. 4 :

Answer with Explanation:

Given : The ratio between the present ages of A and B is 5 : 3

          Let the present age of A is 5x years

          Let the present age of B is 3x years

Given : The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1

A’s age 4 years ago = 5x - 4

B’s age 4 years hence    = 3x + 4               

5x-4  = 1 ; 3x +4  = 1

                   =       1/1

5x-4  = 3x +4  5x – 3x        =       4 + 4  2x =8      x = 4

To find :

5x+4 = ?     :        3x - 4  = ?

20 + 4         =       24 : 12 – 4

24 : 8                3 : 1

 

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