Present ratio of father and son is 6 : 1. After 5 years, their ratio becomes 7 : 2. What is the son’s present age?

Question

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

Accepted Answer

Introduction / Context:This is a classic present-to-future ratio transformation. With present ages in a 6 : 1 ratio, we move five years ahead for both and impose a 7 : 2 ratio. Solving yields the son’s current age. Given Data / Assumptions: Now: father : son = 6 : 1 ⇒ F = 6x, S = x. After 5 years: (F + 5) : (S + 5) = 7 : 2. Find S. Concept / Approach:Substitute F and S and solve via cross-multiplication to find x and then S. Step-by-Step Solution: (6x + 5)/(x + 5) = 7/2 ⇒ 2(6x + 5) = 7(x + 5).12x + 10 = 7x + 35 ⇒ 5x = 25 ⇒ x = 5 ⇒ S = 5. Verification / Alternative check: Present ages: F = 30, S = 5. After 5 years: 35 : 10 = 7 : 2 ✔. Why Other Options Are Wrong: 6, 9, 10 do not satisfy the transformed ratio; the algebra is unique and decisive. Common Pitfalls: Adding 5 to only one person’s age instead of both. Final Answer:5 years

Present ratio of father and son is 6 : 1. After 5 years, their ratio becomes 7 : 2. What is the son’s present age?

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