Ravi’s age is $\frac{3}{5}$ of Shyam’s age. After x years the ratio of the ages of Ravi and Shyam becomes 5 : 7. If initially the sum of their ages is 32, then what is the value of x?

8

Ravi : Shyam 

 3    :   5

⇒ (3 + 5)units = 32

⇒ 8 units = 32

⇒ 1 unit = 4.

After x years,

Ravi : Shyam

  5   :    7

⇒ (5 - 3)units = 2 units = 2 x 4 = 8.

Therefore, value of x is 8.