The average age of a husband and his wife was 23 years at the time of their marriage. After five years, they have a one year old child. What is the current average age of the family?

Introduction / Context:
This is a straightforward average age problem involving a family. You know the average age of a couple at the time of marriage, and a few years later they have a child. You are asked to compute the new average age of the family. Such questions are designed to build comfort with age related word problems and average calculations.

Given Data / Assumptions:
- At the time of marriage, the average age of husband and wife was 23 years.
- Therefore, at marriage, total age of husband and wife together = 2 * 23 = 46 years.
- After 5 years, both husband and wife are 5 years older.
- After 5 years, they have a one year old child.
- We need to find the current average age of the family of three members.

Concept / Approach:
Age problems use the idea that everyone's age increases by the same number of years over any time period. The total age of the couple at marriage is known, so after 5 years, the combined age simply increases by 10 years, because there are 2 persons. Then we add the age of the child to obtain the family total, and divide by the number of family members to get the average age.

Step-by-Step Solution:
Step 1: Total age of husband and wife at marriage = 46 years.Step 2: After 5 years, each of them is 5 years older, so total increase in combined age = 2 * 5 = 10 years.Step 3: Combined age of husband and wife after 5 years = 46 + 10 = 56 years.Step 4: At this time, they have a one year old child, so child age = 1 year.Step 5: Total age of the family now = 56 + 1 = 57 years.Step 6: Number of family members = 3.Step 7: Average age of the family = total age / number of members = 57 / 3 = 19 years.

Verification / Alternative Check:
To verify, think of possible ages. Suppose at marriage the husband was 25 and the wife was 21; that gives an average of 23. After 5 years, they would be 30 and 26, and with a one year old child, the ages would be 30, 26 and 1. The total is 57 and the average is 19, which matches the calculated value. Any specific numbers that respect the original average lead to the same final average.

Why Other Options Are Wrong:
An average of 23 years would mean the total age now is 69, which is too large compared to the original total of 46 plus only 10 additional years for the couple and 1 year for the child. Values 18 or 25 also do not match the correct total of 57 when multiplied by 3.

Common Pitfalls:
Some students forget that the total age of the couple increases by twice the number of years because there are two adults. Others mistakenly take the average of 23 and 1 directly. Carefully tracking totals over time and then dividing by the number of persons avoids these mistakes.

Final Answer:
The current average age of the family is 19 years.