Ages (husband–wife ratio now and after 4 years; marriage-time ratio): The present ratio of a man and his wife is 4 : 3. After 4 years it will be 9 : 7. At the time of marriage their ratio was 5 : 3. How many years ago were they married?

Question

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

Accepted Answer

Introduction / Context:This multi-snapshot problem provides two present/future ratios and an earlier marriage-time ratio. First determine the actual present ages from the now/after-4-years relation; then walk back to the marriage-time ratio to compute the elapsed years since marriage. Given Data / Assumptions: Present: Man : Wife = 4 : 3 ⇒ M = 4k, W = 3k. After 4 years: (4k + 4) : (3k + 4) = 9 : 7. At marriage (t years ago): (M − t) : (W − t) = 5 : 3. Concept / Approach:First solve for k using the “after 4 years” ratio. Then substitute present values into the marriage-time ratio to solve for t, the time elapsed since marriage. Step-by-Step Solution: From after-4-years: 7(4k + 4) = 9(3k + 4) ⇒ 28k + 28 = 27k + 36 ⇒ k = 8. Thus M = 32 and W = 24. Marriage-time condition: (32 − t) : (24 − t) = 5 : 3 ⇒ 3(32 − t) = 5(24 − t) ⇒ 96 − 3t = 120 − 5t ⇒ 2t = 24 ⇒ t = 12. Verification / Alternative check:After 4 years: 36 : 28 reduces to 9 : 7 (✓). Marriage-time ratio 20 : 12 is 5 : 3 (✓). Why Other Options Are Wrong:Any other t fails at least one of the ratio checks when ages are rolled back or forward appropriately. Common Pitfalls:Using the same k at marriage time (ages do not scale; they shift by t), or forgetting to subtract t from both spouses. Final Answer:12 years

Ages (husband–wife ratio now and after 4 years; marriage-time ratio): The present ratio of a man and his wife is 4 : 3. After 4 years it will be 9 : 7. At the time of marriage their ratio was 5 : 3. How many years ago were they married?

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