Present ages of A and B are in the ratio of 3 : 2.  If the present age of C is 45 years and A's present age is \(\frac{4}{5}\) of C's present age, then after how many years the ages of A and B would be in the ratio of 15 : 11?

9

C = 45 years

A = 45 × \(\frac{4}{5}\) = 36 years

Ratio of present age of A and B = 3x  :  2x

⇒ 3x = 36 ⇒ x = 12

Hence, B'age = 2x ⇒ x = 24 years

ATQ, let time is t years:

⇒ \(\frac{36\;+\;t}{24\;+\;t}\) = \(\frac{15}{11}\)

⇒ 396 + 11t = 360 + 15t

⇒ 4t = 36

⇒ t = 9