Five years ago, the average age of a newly married couple was 24 years, but now the average age of the husband, wife and their child is 20 years. The child was born during this 5-year interval. What is the child's present age?

Introduction / Context:
This question tests your understanding of average age problems and how adding a new member to a family affects the overall average. We are given the average age of a couple at the time of marriage and the present average age after the birth of a child, and we must determine the present age of the child.

Given Data / Assumptions:

- Five years ago, the average age of the husband and wife was 24 years.
- Therefore, the total of their ages at that time was 2 × 24 = 48 years.
- The child was born sometime during the last 5 years.
- At present, the average age of the husband, wife and child together is 20 years.
- We need the child's present age in years.

Concept / Approach:
Average age is defined as total age divided by the number of persons. The key idea is to first find the present total age of the couple, then add the child's age and equate it to the present total implied by the new average. From this equation, we can solve for the child's age. The time shift of 5 years must be applied correctly to the ages of the husband and wife only, because the child did not exist throughout the entire interval.

Step-by-Step Solution:
Step 1: Total age of the couple 5 years ago = 2 × 24 = 48 years. Step 2: In 5 years, each of them grows 5 years older, so the present total age of the couple = 48 + (2 × 5) = 48 + 10 = 58 years. Step 3: Let the present age of the child be x years. Step 4: Present total age of the family (husband + wife + child) = 58 + x. Step 5: The present average age of the three is 20 years, so (58 + x) / 3 = 20. Step 6: Multiply both sides by 3 to get 58 + x = 60. Step 7: Therefore, x = 60 − 58 = 2 years.

Verification / Alternative check:
If the child is 2 years old now, then the present ages of the husband and wife must add to 58 years, and including the child gives a total of 60 years. The average for three people is 60 / 3 = 20 years, which matches the statement in the question. This confirms that the child's present age is indeed 2 years.

Why Other Options Are Wrong:
3 years, 4 years, 5 years, and 6 years would lead to present totals of 61, 62, 63, and 64 years respectively, giving averages of more than 20 years. None of these values match the required average of 20 years, so they are incorrect.

Common Pitfalls:
A common error is to forget that both adults age by the full 5 years before the average including the child is calculated. Another mistake is to assume that the child has been present for the entire 5-year period, which is not necessary. Carefully tracking total ages and averages avoids these mistakes.

Final Answer:
The present age of the child is 2 years.