The average age of 5 members of a family is 24 years. The youngest member is 8 years old. What was the average age of the family, in years, at the time of the birth of the youngest member?

Introduction / Context:
Age and average problems are very common in aptitude tests. Here you must understand that when time moves backward, everyone except the newborn becomes younger, and the newborn has age zero at birth. Using this idea, we recalculate the earlier average of the same family.

Given Data / Assumptions:
- Number of family members now = 5. - Present average age = 24 years. - Youngest member is now 8 years old. - We assume that all 5 members were present at the time of birth of the youngest, with the youngest having age zero then.

Concept / Approach:
The present total age can be found by multiplying average by number of members. To go back 8 years, we subtract 8 years from the age of each of the 5 members, which subtracts 5 * 8 from the total age. At that time, the youngest had age zero but is still counted as a member, so we divide the earlier total by 5 to get the required earlier average.

Step-by-Step Solution:
Step 1: Present total age = 5 * 24 = 120 years. Step 2: We go back 8 years to the time of the youngest child birth. Step 3: Each of the 5 members was 8 years younger then. Step 4: Total age decreases by 5 * 8 = 40 years. Step 5: Earlier total age = 120 - 40 = 80 years. Step 6: Number of members then is still 5, including the newborn with age zero. Step 7: Earlier average age = 80 / 5 = 16 years.

Verification / Alternative check:
Move forward from birth to now. Starting from total 80, add 8 years for each of 5 members, which gives 80 + 40 = 120. Average then becomes 120 / 5 = 24, matching the given current average. This confirms that the earlier average of 16 years is consistent with the situation described.

Why Other Options Are Wrong:
- 20, 24 and 30 ignore the effect of subtracting 8 years from all members. - 18 does not lead back to the current average when 8 years are added to each member age.

Common Pitfalls:
A frequent mistake is to subtract 8 only once from the average instead of from each member. Another error is to assume that at the time of birth there were only 4 older members and forget that the newborn is also part of the family, with age zero. Always work with total ages rather than guessing averages directly.

Final Answer:
The average age of the family at the time of the youngest member birth was 16 years.