In an aptitude problem on averages and ages, the average age of 20 students in a group is 21 years. Then 2 students leave the group and 1 new student aged 20 years joins the group, after which the new average age of the group becomes 20 years. If the age of one of the students who left the group was 26 years, what is the age in years of the other student who left the group?

Introduction / Context:
This is a classic averages and ages question. A group of students has a known average age. Some students leave and a new student joins, and the average age of the group changes. From this information, we need to determine the age of one of the students who left. Such questions are very common in quantitative aptitude exams.

Given Data / Assumptions:
- Number of students initially in the group = 20.
- Initial average age = 21 years.
- Two students leave the group.
- One new student of age 20 years joins the group.
- New average age of the group = 20 years.
- Age of one student who left = 26 years.
- We must find the age of the other student who left.

Concept / Approach:
The key idea is that total age = average age * number of persons. We first compute the total age of the group before anyone leaves. Then we compute the total age after the two students leave and the new student joins, using the new average and new number of students. By equating these totals and inserting the known ages, we can solve for the unknown age of the second student who left.

Step-by-Step Solution:
Step 1: Initial total age of 20 students = 20 * 21 = 420 years.Step 2: After two leave and one joins, the new number of students = 20 - 2 + 1 = 19.Step 3: New average age is 20 years, so new total age = 19 * 20 = 380 years.Step 4: Let the age of the unknown student who left be x years.Step 5: Total age after the change = initial total age minus ages of the two who left plus age of new student.Step 6: So 380 = 420 - 26 - x + 20.Step 7: Simplify the right side: 420 - 26 + 20 = 414, so 380 = 414 - x.Step 8: Rearranging gives x = 414 - 380 = 34.Step 9: Therefore the other student who left was 34 years old.

Verification / Alternative check:
Check with concrete totals. Ages removed: 26 and 34, total 60. New student age: 20. Net loss of age = 60 - 20 = 40. Initial total age was 420, so new total should be 420 - 40 = 380. Dividing 380 by the new group size 19 gives 380 / 19 = 20, which matches the new average stated in the question. This confirms that 34 years is correct.

Why Other Options Are Wrong:
Values like 28, 30 or 32 years, when substituted for x, do not give the correct new total of 380 years and therefore do not produce an average of 20 years for 19 students. The option 26 years is the age of the first student who left and cannot also be the age of the second student given the totals involved.

Common Pitfalls:
Students sometimes assume that the number of students remains 20 after the changes or forget to include the age of the new student when recomputing the total. Always track both the total age and the count of people carefully when dealing with average age problems of this type.

Final Answer:
The age of the other student who left the group is 34 years.