Ten years ago, a father’s age was three times his son’s age. Ten years from now, the father’s age will be twice his son’s age. What is the ratio of their present ages (father : son)?

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Two age relations are given at times symmetrically placed around the present: 10 years in the past and 10 years in the future. Modeling with variables and solving yields present ages and their ratio. Given Data / Assumptions: Ten years ago: F − 10 = 3(S − 10). Ten years later: F + 10 = 2(S + 10). Find present ratio F : S. Concept / Approach:Translate each condition into a linear equation in F and S, solve for S, then compute F and simplify the ratio. Step-by-Step Solution: Past: F − 10 = 3S − 30 ⇒ F = 3S − 20.Future: F + 10 = 2S + 20 ⇒ F = 2S + 10.Equate: 3S − 20 = 2S + 10 ⇒ S = 30.Then F = 2S + 10 = 70.Ratio: F : S = 70 : 30 = 7 : 3. Verification / Alternative check: Ten years ago: 60 vs 20 ⇒ father = 3 × son ✔. Ten years hence: 80 vs 40 ⇒ father = 2 × son ✔. Why Other Options Are Wrong: 8 : 5, 5 : 2, 9 : 5 do not satisfy both temporal constraints. Common Pitfalls: Solving only one condition; both must hold simultaneously.Errors when moving from “years ago / hence” to equations. Final Answer:7 : 3

Ten years ago, a father’s age was three times his son’s age. Ten years from now, the father’s age will be twice his son’s age. What is the ratio of their present ages (father : son)?

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