In an ages-in-a-row problem, seven persons are sitting in a single row facing east. The average age of all 7 persons is 26 years. The average age of the first 3 persons (from the left end) is 19 years, and the average age of the last 3 persons (from the right end) is 32 years. What is the age (in years) of the person sitting exactly in the middle position (4th person)?

Introduction:
This question tests the core idea of averages in age problems. When a group average is given, you can convert it into a total sum of ages by multiplying average by number of persons. Then, if partial group averages are given (like first 3 and last 3), you can find their totals and subtract from the overall total to get the missing individual (the middle person).

Given Data / Assumptions:

• Total persons = 7
• Average age of all 7 = 26 years
• Average age of first 3 = 19 years
• Average age of last 3 = 32 years
• Middle person is the 4th person

Concept / Approach:
Total age = average * number of persons. The middle person's age = (total of all 7) - (total of first 3) - (total of last 3).

Step-by-Step Solution:
Total age of all 7 = 26 * 7 = 182Total age of first 3 = 19 * 3 = 57Total age of last 3 = 32 * 3 = 96Middle person's age = 182 - 57 - 96 = 29

Verification / Alternative check:
First 3 + middle + last 3 totals should equal 182. Here 57 + 29 + 96 = 182, so the calculation is consistent.

Why Other Options Are Wrong:
27 years: would make the total 180, not 182.24 years: would make the total 177, not 182.32 years: is the last-3 average value, not the middle person's computed age.30 years: would make the total 183, not 182.

Common Pitfalls:
Using averages directly without converting to totals.Forgetting that the middle person is excluded from both first-3 and last-3 groups.Mixing up position logic in a row (the middle in 7 persons is the 4th person).

Final Answer:
29 years