A man is 3 years older than his wife and four times as old as his son. If the son will be 15 years old after 3 years, what is the present age of the wife?

Introduction / Context:
This aptitude problem connects the ages of a man, his wife and his son through age differences and a future value. We are told that the man is older than his wife and that he is four times as old as his son. The son's future age is given, and we must find the wife's present age.

Given Data / Assumptions:

- The man is 3 years older than his wife.
- The man is four times as old as his son at present.
- The son will be 15 years old after 3 years.
- All ages are measured in years and are positive.

Concept / Approach:
First we use the son's future age to determine his present age. Then we use the multiple relationship to compute the man's present age as a multiple of the son's age. Finally, we use the age difference between the man and his wife to determine the wife's present age. The problem involves basic linear reasoning and proportional relationships between ages.

Step-by-Step Solution:
Step 1: The son will be 15 years old after 3 years. Step 2: Therefore, the son's present age = 15 − 3 = 12 years. Step 3: The man is four times as old as his son. So the man's present age = 4 × 12 = 48 years. Step 4: The man is 3 years older than his wife. Let the wife's present age be W years, so 48 = W + 3. Step 5: Solving for W gives W = 48 − 3 = 45 years.

Verification / Alternative check:
Check all relationships: The son is now 12 years old and will be 15 after 3 years, matching the condition. The man is 48 years old, which is four times 12, so the multiple relationship is correct. The wife is 45 years old, and the man is 3 years older (48 − 45 = 3), confirming the difference. All statements in the problem are satisfied by these ages.

Why Other Options Are Wrong:
Options such as 48, 51, 54 or 60 years for the wife do not maintain the required 3-year difference from the man's age of 48 years while also keeping the man four times as old as the son and the son becoming 15 in 3 years. Only 45 years fits every condition simultaneously.

Common Pitfalls:
Some students mistakenly add 3 instead of subtracting when calculating the wife's age from the man's age. Others may forget to convert the son's future age into his present age before applying the "four times" multiplier. Always move step by step: find present ages first, then apply relationships.

Final Answer:
The present age of the wife is 45 years.