Five years ago, the average age of a family consisting of a father, a mother and a son was 35 years. Three years ago, the average age of the father and the mother was 46 years. What is the present age, in years, of the son?

Introduction / Context:
This question combines average age information at two different times for a small family. It is a standard type of problem where the average of all three members is given for one time in the past, and the average of only the parents is given for another time. From this information, we have to deduce the current age of the son. It requires careful use of the average formula and the understanding that all members age equally over time.

Given Data / Assumptions:

• Five years ago, the family consisted of father, mother and son and their average age was 35 years.
• Three years ago, the average age of the father and the mother alone was 46 years.
• We need the present age of the son.
• Ages are measured in years and are positive.

Concept / Approach:
We use the average at each time to calculate the total ages of the corresponding group. At five years ago, we get the combined total of all three. At three years ago, we get the combined total of the parents only. By moving these totals forward to the present time by adding the appropriate number of years for each person, we can find the present total of all three and the present total of the parents. The difference between these totals gives the present age of the son.

Step-by-Step Solution:
Step 1: Five years ago, the average age of the father, mother and son was 35 years for 3 people. Step 2: The total age of the three family members five years ago was 35 * 3 = 105 years. Step 3: From five years ago to the present, each of the three persons has aged 5 years, increasing the total age by 3 * 5 = 15 years. Step 4: Therefore, the total present age of the three family members is 105 + 15 = 120 years. Step 5: Three years ago, the average age of the father and the mother was 46 years for 2 people. Step 6: The combined age of the parents three years ago was 46 * 2 = 92 years. Step 7: From three years ago to now, both parents have aged 3 years each, so the total age of the parents has increased by 2 * 3 = 6 years. Step 8: Hence the present combined age of the father and the mother is 92 + 6 = 98 years. Step 9: The present age of the son is obtained by subtracting the parents present total from the family present total: 120 - 98 = 22 years. Step 10: Therefore, the son present age is 22 years.

Verification / Alternative check:
We can check by reconstructing the ages backwards. If the son present age is 22 years, then five years ago he was 17 years old. Suppose the present total of the parents is 98 years, so five years ago their combined age was 98 - 10 = 88 years. At that time, the total age of the family was 88 + 17 = 105 years, matching the earlier calculation of 105. Three years ago, the parents combined age would have been 98 - 6 = 92 years, giving an average of 92 / 2 = 46 years, which agrees with the given data. This confirms the solution.

Why Other Options Are Wrong:
Option A (20 years) does not produce consistent totals when checked against both average conditions.
Option B (24 years) gives a different present total, and when taken back five and three years, breaks at least one of the average relationships.
Option C (26 years) also fails to satisfy both the five year and three year average constraints simultaneously.

Common Pitfalls:
Students may incorrectly apply the average formula or forget to add the correct number of years to move from a past time to the present. Another common mistake is to assume that the average remains constant over time, which is not the case here. Always compute total ages first from averages, then adjust those totals by adding or subtracting the appropriate time for each person before making comparisons.

Final Answer:
The present age of the son is 22 years.