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?

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:

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