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The age of a father 3 years ago is same as the age of a mother 3 years after, and the ratio of the ages of the father 2 years and son 4 years after is 10 ∶ 3. What is the ratio of age of the mother after 3 years and the son after 2 years if the present age of the mother is 4 times the age of the son?

The age of a father 3 years ago is same as the age of a mother 3 years after, and the ratio of the ages of the father 2 years and son 4 years after is 10 ∶ 3. What is the ratio of age of the mother after 3 years and the son after 2 years if the present age of the mother is 4 times the age of the son? Correct Answer 7 ∶ 2

The ratio age of father 2 years and son 4 years after is 10 ∶ 3

⇒ The present age of the father = 10x – 2

The present age of the son = 3x – 4

The present age of the mother is 4 times that of son

⇒ Present age of the mother = 4(3x – 4) = 12x – 16

The age of the father 3 years ago is same as the age of the mother 3 years after

⇒ 10x – 2 – 3 = 12x – 16 + 3 

⇒ 2x = 8

⇒ x = 4

∴ The present age of the mother = 12 × 4 – 16 = 32

The present age of the son = 3 × 4 – 4 = 8

∴ The ratio of age of mother after 3 years and son after 2 years

⇒ (32 + 3)/(8 + 2) = 35/10 = 7/2 or 7 ∶ 2

∴ The ratio of age of mother after 3 years and son after 2 years is 7 ∶ 2

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