Question

The present ages of A and B are in the ratio 4:5. After 6 years, their ages will be in the ratio 5:6. Find A's present age.

Solution

1. Let their present ages be 4x and 5x.
2. After 6 years, (4x + 6)/(5x + 6) = 5/6.
3. 6(4x + 6) = 5(5x + 6), so 24x + 36 = 25x + 30.
4. x = 6, so A's present age is 4 x 6 = 24 years.