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The ratio of the age of P five years ago to the age of Q five years hence is 2:3. The ratio of the present age of Q to the present age of R is 11:15. If the sum of the present ages of P and R is 120, and the age of P y years after and the age of Q 5 years after are in the ratio 1:1, find the value of y.

1. 20
2. 18
3. 16
4. 12

Correct answer: 16

Solution

Let present ages be P, Q, and R. From the given ratios and sum, we can form simultaneous equations and solve for the present ages. Substituting into the condition that P's age after y years equals Q's age after 5 years gives y = 16.

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