Question

The ages of A and B are in the ratio 7:5.Ten years hence, the ratio of their ages will be 9:7. Find their ages.

Answer 1

Given, the present ages of A and B are in the ratio 7 : 5.
∴ Their present ages are 7x : 5x.
After 10 years, their ages will be :
(7x + 10) and (5x + 10) respectively.
New ratio of their ages = 9 : 7
As per given conditions,

`((7x + 10))/((5x + 10)) = (9)/(7)`
⇒ 7(7x + 10) = 9(5x + 10)
⇒ 49x + 70 = 45x + 90
⇒ 4x = 20
⇒ x = 5 years.
Thus, the present ages of A and B are 35 and 25 respectively.