Question

The ratio of the present ages of two friends is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years?

Answer 1

Answer:

Let their present ages be x and y years.

Clearly x/y=2/3 as given

=> 3x=2y

Again six years ago their ages were (x- 6 )and (y-6 )years respectively.

Clearly, ((x-6)/(y-6)=1/3

=>3x-18=y-6

=>3x-y= 12

Thus we have two equations:

3x=2y. (1)

3x-y=12. (2)

Substituting 3x=2y in the second equation we have

2y-y=12 or y=12

Thus the age of the second friend is 12 years at present.

Substituting y=12 in the second equation (2) we have

3x-y=12

=> 3x-12=12

=> 3x=24

=> X=8

Thus the first friend is 8 years old at present.

After 4 years their ages will be 12 years and 16 years respectively

Hence required ratio = 12:16= 3:4

Thus the answer is 3:4.