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At present, the ratio of the ages of P and Q is 3 : 5, the ratio of ages of Q and R is 3 : 4 and the ratio of ages of R and S is 10 : 11. If the sum of the present ages of all of them is 198 years, what is the ratio of ages of Q and R after 15 years?

At present, the ratio of the ages of P and Q is 3 : 5, the ratio of ages of Q and R is 3 : 4 and the ratio of ages of R and S is 10 : 11. If the sum of the present ages of all of them is 198 years, what is the ratio of ages of Q and R after 15 years? Correct Answer 4 : 5

Let the present ages of P, Q, R and S be ‘p’, ‘q’, ‘r’ and ‘s’ years respectively.

p : q = 3 : 5, q : r = 3 : 4 and r : s = 10 : 11

p : q = 9 : 15 and q : r = 15 : 20

p : q : r = 9 : 15 : 20 and r : s = 20 : 22

∴ p : q : r : s = 9 : 15 : 20 : 22

Let them be 9k, 15k, 20k and 22k years respectively.

9k + 15k + 20k + 22k = 198

⇒ 66k = 198

⇒ k = 3

Present ages of Q and R is 45 years and 60 years respectively.

Ratio of their ages after 15 years = 60 : 75 = 4 : 5

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