A man was 32 years old when his first son was born. His wife was 35 years old when the son was 7 years old. What is the difference between the age of the father and the age of the mother in years?

Introduction / Context:
This question involves a family age relationship among a father, a mother, and their son. The ages of the parents are given at specific times relative to the son's birth and childhood. From these, we have to find the constant age difference between the father and the mother. Problems like this test understanding of how age differences remain constant over time.

Given Data / Assumptions:
- The father was 32 years old when his first son was born.
- When the son was 7 years old, the mother was 35 years old.
- Ages are in years.
- We need the difference between the age of the father and the age of the mother.

Concept / Approach:
The key concept is that the difference in age between any two people does not change over time. Instead of tracking ages year by year, we can find the ages of the father and mother at one common time and compute their difference. Here, the natural common reference point is the time when the son is 7 years old, since both parents' ages are easy to express then.

Step-by-Step Solution:
Step 1: At the time the son was born, the father was 32 years old.Step 2: When the son is 7 years old, 7 years have passed since his birth.Step 3: Therefore, when the son is 7, the father's age is 32 + 7 = 39 years.Step 4: The problem states that when the son is 7 years old, the mother is 35 years old.Step 5: At that same time, the difference between the father's age and the mother's age is 39 - 35.Step 6: Compute this difference: 39 - 35 = 4 years.Step 7: Because age differences do not change over time, the father is always 4 years older than the mother.

Verification / Alternative check:
We can check consistency at both time points. At the time of the son's birth, if the father is 32 and the mother is 28, their difference is 4 years. Seven years later, the father would be 39 and the mother 35, again a difference of 4 years. This matches the given information that the mother is 35 when the son is 7 and confirms that the age difference is 4 years in every time frame.

Why Other Options Are Wrong:
A difference of 7, 5, 3, or 2 years would not fit the data. For instance, if the difference were 7 years, the mother would have to be 32 years old when the son was 7, which contradicts the given information that she was 35 at that time. Only a 4 year difference is consistent with the ages provided at the specific milestone when the son is 7 years old.

Common Pitfalls:
Some learners get confused and try to track the ages from the father's perspective only, without using the second piece of information about the mother. Others mistakenly think that the difference between the parents' ages might change over time. Remember that while ages increase, the difference between them always stays the same. Focusing on a single reference time where both ages are known makes the problem simple.

Final Answer:
The difference between the age of the father and the age of the mother is 4 years.