Age Difference — “A man was 31 when his first son was born. When the son turned 7, the wife was 26. What is the age difference between the man and his wife?”

Introduction / Context:
We are asked for a fixed age difference based on two anchored events: the son’s birth and the time the son reaches 7. Aligning both events lets us compute both parents’ ages at birth and subtract.

Given Data / Assumptions:

• At son’s birth: father = 31 (given).
• At son age 7: wife = 26 ⇒ wife at birth = 26 − 7 = 19.
• Age difference = father_at_birth − wife_at_birth.

Concept / Approach:
Because both ages are rolled back by the same number of years (7) to the birth event, the difference computed there is the same as the present difference. Use the birth event to avoid extra unknowns.

Step-by-Step Solution:

Verification / Alternative check:
Any time later the difference remains 12 because age gaps are invariant over time.

Why Other Options Are Wrong:
5/6/7/9 do not match the invariant gap based on the anchored birth event data.

Common Pitfalls:
Adding 7 instead of subtracting; computing difference at two different time points for the two parents.

Final Answer:
12 years