The present average age of a family of five members is 26 years. If the present age of the youngest member is 10 years, what was the average age of the family at the time of the youngest member's birth, assuming nobody has died in the family since then?

Introduction / Context:
This problem tests understanding of average ages over time and how the birth of a new member affects the family average. We compare the present situation with the situation 10 years ago when the youngest member was just born. The key idea is to track total ages rather than only averages.

Given Data / Assumptions:

• There are 5 family members at present.
• The present average age of the family is 26 years.
• The youngest member is currently 10 years old.
• No death has occurred in the family since the birth of the youngest member.
• We need the average age of the family at the time of the youngest member's birth.

Concept / Approach:
First find the total present age of all 5 members using the average. Then subtract the years that have passed for each member to move back in time to the year of birth of the youngest child. At that time there were only 4 members, because the youngest was just born. We then compute the average from the total age of those 4 members at that earlier time.

Step-by-Step Solution:
Present average age of 5 members = 26 years. Total present age of family = 26 * 5 = 130 years. Present age of youngest member = 10 years. The sum of the present ages of the other 4 members = 130 - 10 = 120 years. The youngest member was born 10 years ago, so move 10 years back. Ten years ago, each of the older 4 was 10 years younger, so their total then = 120 - 4 * 10 = 120 - 40 = 80 years. At the time of birth, the youngest member was 0 years old, so total age of family = 80 years with 4 members. Average age at that time = 80 / 4 = 20 years.

Verification / Alternative check:
Check by moving forward: Ten years ago total = 80. After 10 years, each of 4 older members gains 10 years, adding 40, and the youngest reaches 10, adding 10 more. New total = 80 + 40 + 10 = 130, giving present average 130 / 5 = 26 as stated. This confirms that the earlier average 20 years is consistent.

Why Other Options Are Wrong:
An average of 19 or 18 years would not produce the correct present total when progressed by 10 years. A value like 16 years is far too low and leads to a wrong total when ages are advanced. The option 21 years also fails when the same forward check is done. Only 20 years yields the correct present situation.

Common Pitfalls:
Many learners mistakenly average only the remaining four members directly or think that the average decreases by 10, which is incorrect. Another error is forgetting that the youngest was 0 years at birth, not 10. Working with totals and carefully counting the number of family members at each time avoids these misconceptions.

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