The present ages of three persons are in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Question: The present ages of three persons are in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Solution:
Let the present ages of the three persons be 4x, 7x, and 9x years.
Eight years ago, their ages were,
(4x - 8), (7x - 8) and (9x - 8)

According to the problem,
⇒ (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x - 24 = 56
⇒ 20x = 80
⇒ x = 80/20
∴ x = 4
∴ First person = 4x = 4 × 4 = 16 years
∴ Second person = 7x = 7 × 4 = 28 years
∴ Third person = 9x = 9 × 4 = 36 years

So, the present ages of the three persons are 16 years, 28 years, and 36 years respectively