Difficulty: Medium
Correct Answer: 14 years, 10 years
Explanation:
Introduction / Context:This problem gives ratios at two different time points, which is neatly handled by parameterizing the earlier ages and then advancing each by the same elapsed time.
Given Data / Assumptions:
Concept / Approach:Let R − 2 = 3k and M − 2 = 2k. Then R = 3k + 2, M = 2k + 2. Impose the present ratio to solve for k.
Step-by-Step Solution:
1) Set R = 3k + 2 and M = 2k + 2. 2) Apply present ratio: (3k + 2) / (2k + 2) = 7 / 5. 3) Cross-multiply: 5(3k + 2) = 7(2k + 2) → 15k + 10 = 14k + 14 → k = 4. 4) Present ages: R = 3*4 + 2 = 14 years; M = 2*4 + 2 = 10 years.Verification / Alternative check:Two years ago they were 12 and 8, which reduce to 3 : 2; now they are 14 and 10 → 7 : 5.
Why Other Options Are Wrong:They violate one of the two ratio constraints when checked.
Common Pitfalls:Forgetting to add the same 2 years to both persons, or swapping roles of Ram and Mohan when mapping ratios.
Final Answer:14 years, 10 years
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