The ratio of the present age of A to that of B is 7:9. Six years ago the ratio of 1/3 of A’s age at that time and 1/3 of B’s age at that time was 1:3. What will be the ratio of A’s age to B’s age 5 years from now?

Let the present age of A and B be 7x and 9x respectively. Now, (1/3(7x-6))/(1/3(9x-6))= 1/3 So ((7x-6))/((9x-6)) = 1/3 ⇒ 21x – 18 = 9x – 6 ⇒ 12x = 12 ∴ x = 1 ∴ 5 years from now, A’s age = 7x + 5 = 7 + 5 = 12 years B’s age = 9x + 5 = 14 years ∴ Required ratio = 12/14 = 6:7

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