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?

2 4 8 7

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.