Ages — two time-shifted ratios (solve for Shyam): Four years ago Shyam was 3/4 of Ram. Four years hence Shyam will be 5/6 of Ram. Find Shyam’s present age.
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
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A15 yr
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B20 yr
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C16 yr
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D24 yr
Answer
Correct Answer: 16 yr
Explanation
Introduction / Context:Two distinct time-shifted ratios give two equations. Solve them to find the current ages consistently.
Given Data / Assumptions:
- Shyam − 4 = (3/4)(Ram − 4).
- Shyam + 4 = (5/6)(Ram + 4).
Concept / Approach:Let S and R be present ages. Use elimination or substitution across the two linear equations.
Step-by-Step Solution:
S − 4 = (3/4)(R − 4).S + 4 = (5/6)(R + 4).Solving yields R = 20, S = 16.Verification / Alternative check:
Four years ago: 12 vs 16 ⇒ 12/16 = 3/4 ✓; four years hence: 20 vs 24 ⇒ 20/24 = 5/6 ✓Why Other Options Are Wrong:
- 15, 20, 24 do not satisfy both time-shift conditions for S.
Common Pitfalls:
- Mistaking who is the numerator in each ratio.
Final Answer:16 yr