A is twice as old as B was two years ago. The difference between their present ages is 2 years. Find A’s present age (in years).
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
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A14 years
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B18 years
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C8 years
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D12 years
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ENone of these
Answer
Correct Answer: 8 years
Explanation
Introduction / Context:Mixing a present-time difference with a past-time multiplicative relation yields a solvable two-equation system in present ages A and B.
Given Data / Assumptions:
- A = 2(B − 2)
- A − B = 2
Concept / Approach:Substitute the expression for A from the first equation into the second and solve for B; then recover A.
Step-by-Step Solution:
A = 2B − 4(2B − 4) − B = 2 ⇒ B − 4 = 2 ⇒ B = 6A = 2B − 4 = 12 − 4 = 8 yearsVerification / Alternative check:B two years ago = 4; 2 × 4 = 8 = A now; and A − B = 2 holds (8 − 6).
Why Other Options Are Wrong:12, 14, 18 violate either the difference or the past-time doubling relation.
Common Pitfalls:Doubling B now instead of B two years ago, or misapplying the 2-year difference sign.
Final Answer:8 years.