Sonali is 40 years old and Nitya is 60 years old. How many years ago was the ratio of their ages 3 : 5?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 years
Both ages fall by the same number of years as we go back in time. Let that number be \(x\); the ages \(x\) years ago are then set in the ratio 3 : 5.
Ages \(x\) years ago: Sonali \(40-x\), Nitya \(60-x\)
\(\displaystyle \frac{40-x}{60-x}=\frac{3}{5}\)
\(200-5x=180-3x\)
\(2x=20\), so \(x=10\)
Shortcut: The age difference never changes; it is 20 years.
In the ratio 3 : 5 the difference is 2 parts, so 2 parts = 20 years and 1 part = 10 years
Sonali’s age then was 3 parts = 30, which is 10 years less than 40