Eight years ago, the ages of Kiran and Sanjay were in the ratio $4 : 3$. Four years from now, the ratio will be $7 : 6$. What is the sum of their present ages?

Explanation

1. 01

   Eight years ago the ages were $4k$ and $3k$; four years from now they are $4k + 12$ and $3k + 12$.

2. 02

   $\frac{4k + 12}{3k + 12} = \frac{7}{6}$, so $24k + 72 = 21k + 84$ and $k = 4$.

3. 03

   Eight years ago: 16 and 12. Now: 24 and 20.

4. 04

   Sum now = $24 + 20 = 44$ years.