Problems on Ages — “The sum of the ages of Ram, Shyam and Mohan is 93. Ten years ago their ratio was 2 : 3 : 4. Find Mohan’s present age.”
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A38 years
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B34 years
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C32 years
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D24 years
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E36 years
Answer
Correct Answer: 38 years
Explanation
Introduction / Context:A common structure is a present total with a ratio given at an earlier time. Represent past ages via parts, advance them by the elapsed years to the present, and match the current total.
Given Data / Assumptions:
- Ten years ago: Ram : Shyam : Mohan = 2 : 3 : 4 ⇒ let past ages be 2k, 3k, 4k.
- Now: each has aged 10 years, and the present total = 93.
Concept / Approach:Present ages are (2k + 10), (3k + 10), (4k + 10). Sum and solve for k, then compute Mohan’s present age (the third term).
Step-by-Step Solution:
(2k + 10) + (3k + 10) + (4k + 10) = 93.9k + 30 = 93 ⇒ 9k = 63 ⇒ k = 7.Mohan now = 4k + 10 = 28 + 10 = 38 years.Verification / Alternative check:Present ages become (24, 31, 38); ten years ago they were (14, 21, 28) = 2 : 3 : 4 ✓; present sum 24 + 31 + 38 = 93 ✓.
Why Other Options Are Wrong:34/32/24/36 do not align with both the past ratio and the present total when back-checked.
Common Pitfalls:Applying the +10 only once to the total instead of per person (+30 overall); mixing present and past parts in the same equation.
Final Answer:38 years