Sunil is 40 years old and Anil is 60 years old today. How many years ago was the ratio of their ages 3:5?
Verbal Reasoning
Problems on Ages
Difficulty: Easy
Choose an option
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A5 years
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B10 years
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C12 years
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D15 years
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ENone of these
Answer
Correct Answer: 10 years
Explanation
Introduction / Context:This is a standard back-dating age ratio problem. We translate “x years ago” into (present age − x) and impose the ratio.
Given Data / Assumptions:
- Present ages: Sunil = 40, Anil = 60
- We seek x such that (40 − x) : (60 − x) = 3 : 5
Concept / Approach:Use the ratio definition and cross-multiply to form a linear equation in x. Solve for x and ensure it is feasible (nonnegative and less than both present ages).
Step-by-Step Solution:
(40 − x) / (60 − x) = 3/55(40 − x) = 3(60 − x)200 − 5x = 180 − 3x200 − 180 = 5x − 3x ⇒ 20 = 2x ⇒ x = 10Verification / Alternative check:
10 years ago: 30 and 50 ⇒ 30:50 = 3:5 ✓Why Other Options Are Wrong:
- 5, 12, 15 years: Substituting these values will not yield the ratio 3:5.
- None of these: We have a valid solution at 10 years.
Common Pitfalls:Setting (older − x)/(younger − x) to the inverse ratio; or forgetting that the same x is subtracted from both ages in the past scenario.
Final Answer:10 years