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Currently, P's age is three times Q's age. R is 5 years older than Q. The combined age of P, Q, and R is 75 years. What is the ratio of Q's age 5 years ago to P's age 3 years from now?

1. 1 : 4
2. 2 : 3
3. 1 : 5
4. 4 : 7

Correct answer: 1 : 5

Solution

Let Q = x. Then P = 3x and R = x+5. Sum: 3x + x + x + 5 = 75 → 5x = 70 → x = 14. So Q=14, P=42, R=19. Q five years ago = 9; P three years from now = 45. Ratio = 9:45 = 1:5.

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