After 10 years, A will be twice as old as B was 10 years ago. If A is currently 9 years older than B, what is B's present age?
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
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A19 years
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B29 years
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C39 years
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D49 years
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ENone of these
Answer
Correct Answer: 39 years
Explanation
Introduction / Context:This problem mixes a future age with a past age and adds a present-age difference. Carefully track times for both people and set up precise equations.
Given Data / Assumptions:
- Let present ages be A and B.
- After 10 years: A + 10 = 2(B − 10)
- Now: A = B + 9
Concept / Approach:Substitute A = B + 9 into the future–past relation to produce a single linear equation in B. Solve for B, then verify with both statements.
Step-by-Step Solution:
(B + 9) + 10 = 2(B − 10)B + 19 = 2B − 2039 = B ⇒ B = 39Then A = B + 9 = 48Verification / Alternative check:
After 10 years: A = 58; B ten years ago: 29 ⇒ 58 = 2 × 29 ✓Why Other Options Are Wrong:
- 19, 29, 49 do not satisfy both constraints.
- None of these is unnecessary since 39 works.
Common Pitfalls:Using A + 10 = 2(B + 10) (wrong time reference for B); or mistakenly setting A − B = 9 after shifting the timeline rather than at present only.
Final Answer:39 years