The ratio of the ages of two boys is 3 : 4. After 3 years, the ratio will be 4 : 5. The ratio of their ages after 21 years will be

Given Ratio of Ages is 3 : 4

Let the common factor be x

∴ Ages of the boys are 3x and 4x respectively.

After 3 years their ages would be 3x + 3 and 4x + 3

⇒ After 3 years their Ratio will be 4 : 5

⇒ (3x + 3)/(4x + 3) = 4/5

⇒ 5(3x + 3) = 4(4x + 3)

⇒ 15x + 15 = 16x + 12

⇒ x = 3

∴ Ages of boys are 9 years and 12 years.

Their Ages after 21 years would be 30 years and 33 years.

Ratio = 30/33 = 10/11 = 10 : 11