Vikram is three times as old as his niece Tara. In 15 years, the ratio of their ages will be $3 : 2$. How old is Vikram now?

Explanation

1. 01

   Let Tara be $t$ and Vikram $3t$.

2. 02

   $\frac{3t + 15}{t + 15} = \frac{3}{2}$, so $6t + 30 = 3t + 45$.

3. 03

   $t = 5$, so Vikram is 15 years old.

4. 04

   Check: in 15 years they are 30 and 20, a ratio of $3 : 2$.