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 at the time of the youngest member's birth?

Introduction / Context:
This problem involves backward reasoning with averages and ages. You are given the present average age of a family, the current age of the youngest member, and you must find the family average at the time of that child's birth. Age problems of this type appear frequently in aptitude tests and require careful thinking about how ages change over time.

Given Data / Assumptions:

• Number of family members now = 5.
• Current average age = 24 years.
• Youngest member's current age = 8 years.
• At the time of the youngest member's birth, there were only 4 family members.
• The ages of those 4 members were each 8 years less than their current ages.

Concept / Approach:
The idea is to first find the current total age of all 5 members. Then subtract the youngest member's age to get the combined age of the other four. To find their total age 8 years ago, we subtract 8 years from each of these four members, effectively subtracting 4 * 8 from that total. This gives the total age of the family at the time of birth, and dividing by 4 yields the required average.

Step-by-Step Solution:
Step 1: Current total age of 5 members = 5 * 24 = 120 years.Step 2: Current age of youngest member = 8 years.Step 3: Combined current age of the other 4 members = 120 − 8 = 112 years.Step 4: 8 years ago, each of these 4 members was 8 years younger, so total reduction in their combined ages = 4 * 8 = 32 years.Step 5: Total age of the family at the time of the youngest member's birth = 112 − 32 = 80 years.Step 6: Average age then = 80 / 4 = 20 years.

Verification / Alternative check:
We can move forward from the time of birth. If the average age of 4 members then was 20, total = 80. After 8 years, each gains 8 years, so total gained = 4 * 8 = 32 and new total becomes 112. Adding the youngest member now aged 8 gives 120, which divided by 5 gives the current average of 24. This confirms that our reasoning is correct.

Why Other Options Are Wrong:
An average of 16 or 18 years would not grow to give the correct current totals when moved forward by 8 years and combined with the child. An average of 24 or 30 years at birth is not realistic since people were younger at that time and would produce incorrect current averages.

Common Pitfalls:

• Forgetting that the youngest member did not exist at the time of birth and mistakenly dividing by 5 instead of 4.
• Subtracting 8 years only once instead of for each of the 4 older members.
• Confusing current averages with past averages without adjusting ages.

Final Answer:
The average age of the family at the time of the youngest member's birth was 20 years.