One year ago, the father was four times as old as his son. Six years from now, the father will be 9 years more than twice his son’s age. What is the ratio of their present ages (father : son)?
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
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A13 : 4
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B12 : 5
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C11 : 3
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D9 : 2
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ENone of these
Answer
Correct Answer: 11 : 3
Explanation
Introduction / Context:We have two time-shifted linear relations: one from the past comparing father to son by a factor, and another from the future comparing father to twice the son plus a fixed number. Solve these equations to obtain current ages and then simplify the ratio.
Given Data / Assumptions:
- One year ago: F − 1 = 4(S − 1).
- Six years later: F + 6 = 2(S + 6) + 9.
- Find present ratio F : S.
Concept / Approach:Form linear equations in F and S and solve. The presence of constants (−1, +6, +9) requires careful algebra to avoid mistakes.
Step-by-Step Solution:
From the past: F − 1 = 4S − 4 ⇒ F = 4S − 3.From the future: F + 6 = 2S + 21 ⇒ F = 2S + 15.Equate: 4S − 3 = 2S + 15 ⇒ 2S = 18 ⇒ S = 9 ⇒ F = 33.Ratio F : S = 33 : 9 = 11 : 3.Verification / Alternative check:
One year ago: 32 vs 8 ⇒ father = 4 × son ✔. Six years later: 39 vs 15 ⇒ 39 = 2 × 15 + 9 ✔.Why Other Options Are Wrong:
13 : 4, 12 : 5, 9 : 2 contradict one or both time-shifted conditions.Common Pitfalls:
Mishandling the constants −1, +6, and +9 when translating to equations.Final Answer:11 : 3