Difficulty: Medium
Correct Answer: None of these
Explanation:
Introduction / Context:Two ratios at different times generate a 2×2 linear system in present ages. Solve systematically and check whether the resulting integer matches any listed options; if not, select “None of these.”
Given Data / Assumptions:
Concept / Approach:Convert ratios to linear equations by cross-multiplication and then solve simultaneously for A and B.
Step-by-Step Solution:
4(A − 1) = 3(B − 1) ⇒ 4A − 3B = 16(A + 1) = 5(B + 1) ⇒ 6A − 5B = −1Solve: A = 4, then 4A − 3B = 1 ⇒ 16 − 3B = 1 ⇒ B = 5Verification / Alternative check:Check both ratios: (4−1):(5−1)=3:4 and (4+1):(5+1)=5:6 ✓.
Why Other Options Are Wrong:8, 4, and 6 do not equal the computed B = 5; hence “None of these.”
Common Pitfalls:Sign errors when shifting ages by ±1; misapplying ratios to present instead of past/future ages.
Final Answer:None of these (B’s present age is 5 years).
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