A and B currently have an age ratio of 7 : 3. After 7 years this age ratio will become 2 : 1. After how many years from now will the age ratio between the ages of A and B become 3 : 2 ?

35 years

ATQ,

Lets assume present age of A and B is 7x and 3x respectively.

Given, after seven years ratio between their ages will be, \(\frac{7x + 7}{3x + 7}\) = \(\frac{2}{1}\)

⇒ 7x + 7 = 6x + 14

   x = 7

So, present age of A = 49

      Present age of B = 21

Lets assume after y years ratio between their ages will be 3:2

⇒ \(\frac{49 + y}{21 + y}\) = \(\frac{3}{2}\)

⇒ 98 + 2y = 63 + 3y

   y = 35

So after 35 years ratio between the ages of A and B will be 3:2