Present ages are in the ratio 2 : 5 (A : B). After 8 years, their ages will be in the ratio 1 : 2. What is the difference between their present ages?

Question

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

Accepted Answer

Introduction / Context:Ratios of ages at two different times allow us to parameterize present ages and apply a future ratio condition. We then compute the numeric ages and their difference. Given Data / Assumptions: Now: A : B = 2 : 5 ⇒ A = 2x, B = 5x. After 8 years: (A + 8) : (B + 8) = 1 : 2. Find the present-age difference B − A. Concept / Approach:Substitute A = 2x and B = 5x into the future ratio and solve for x. The present difference is (5x − 2x). Step-by-Step Solution: (A + 8)/(B + 8) = 1/2 ⇒ 2(A + 8) = (B + 8).2(2x + 8) = 5x + 8 ⇒ 4x + 16 = 5x + 8 ⇒ x = 8.Present ages: A = 16, B = 40. Difference = 24 years. Verification / Alternative check: After 8 years: A = 24, B = 48 ⇒ 24 : 48 = 1 : 2 ✔. Why Other Options Are Wrong: 20, 26, 29 are inconsistent with the future ratio. Common Pitfalls: Forgetting to add 8 to both ages when forming the future ratio.Assuming the difference remains proportional (it does not; it is absolute). Final Answer:24 years

Present ages are in the ratio 2 : 5 (A : B). After 8 years, their ages will be in the ratio 1 : 2. What is the difference between their present ages?

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