Present ages of A and B are in the ratio of 13 : 7 .  If the present age of C is 39 years and A's present age is \(\frac{4}{3}\) of C's present age, then after how many years the ages of A and B would be in the ratio of 5 : 3 ?

8 years 

C = 39 years

A = 39 × \(\frac{4}{3}\) = 52 years

Ratio of present age of A and B = 13x  :  7x

⇒ 13x = 52 ⇒ x = 4

Hence, B'age  ⇒ 7x = 28 years

ATQ, let time is t years:

⇒ \(\frac{52\;+\;t}{28\;+\;t}\) = \(\frac{5}{3}\)

⇒ 156 + 3t = 140 + 5t

⇒ 2t = 16

⇒ t = 8