P is 40 years old and Q is 60 years old. How many years ago was the ratio of their ages 3 : 5 ? Option 1: 5 years Option 2: 10 years Option 3: 15 years Option 4: 20 years

Answer: 10 years. Solution: Let x years ago their ages be (40-x) and (60-x). Then (40-x)/(60-x) = 3/5. Cross-multiplying: 5(40-x) = 3(60-x), so 200 - 5x = 180 - 3x, giving 2x = 20, so x = 10, which matches option 2.

Arithmetic

Ratio, Proportion & Variation

Medium

P is 40 years old and Q is 60 years old. How many years ago was the ratio of their ages 3 : 5 ?

5 years

10 years

15 years

20 years

✅ Correct Option: 2

Let $x$ years ago their ages be $(40-x)$ and $(60-x)$ . Then $\frac{40-x}{60-x} = \frac{3}{5}$ . Cross-multiplying: $5(40-x) = 3(60-x)$ , so $200 - 5x = 180 - 3x$ , giving $2x = 20$ , so $x = 10$ , which matches option 2.

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