The ratio of the ages of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their ages after 10 years will be

Given:

Current age ratio = 5:6

After 2 years, ratio = 7:8

Calculations

Let present ages be 5x and 6x

Then, after 2 years: (5x + 2)/(6x + 2) = 7/8

Find x, then compute ages after 10 years and find the ratio

⇒ (5x + 2)/(6x + 2) = 7/8

⇒ 8(5x + 2) = 7(6x + 2)

⇒ 40x + 16 = 42x + 14

⇒ 2x = 2

⇒ x = 1

Present ages = 5x = 5, 6x = 6

After 10 years = 5 + 10 = 15, 6 + 10 = 16

∴ The ratio of their ages after 10 years will be 15:16.