The average age of 80 boys in a class is 15 years. The average age of a group of 15 boys is 16 years and the average age of another group of 25 boys is 14 years. What is the average age of the remaining boys in the class?

Introduction / Context:
This problem is a classic example of weighted averages and group averages. You are given the overall average of a large group and the averages of two subgroups, and you must determine the average of the remaining subgroup. This type of question is common in aptitude tests to assess your ability to combine and separate averages correctly.

Given Data / Assumptions:

• Total number of boys = 80.
• Overall average age = 15 years.
• First subgroup: 15 boys with average age = 16 years.
• Second subgroup: 25 boys with average age = 14 years.
• Remaining boys = 80 - (15 + 25) = 40 boys.

Concept / Approach:
The main idea is that average = total sum / number of items. We first find the total age of all 80 boys using the overall average. Then we compute the total age of the two known subgroups from their averages. Subtracting these totals from the overall total gives the combined age of the remaining boys, which then yields their average.

Step-by-Step Solution:
Step 1: Total age of all 80 boys = 80 * 15 = 1200 years.Step 2: Total age of first 15 boys = 15 * 16 = 240 years.Step 3: Total age of second 25 boys = 25 * 14 = 350 years.Step 4: Combined age of these 40 boys = 240 + 350 = 590 years.Step 5: Age of remaining 40 boys = 1200 - 590 = 610 years.Step 6: Average age of remaining 40 boys = 610 / 40 = 15.25 years.

Verification / Alternative check:
We can quickly verify by recombining. The remaining group has total age 610 years, so adding 610 + 590 gives 1200, which matches the original total. Dividing 1200 by 80 again yields 15 years as the overall average, confirming that the computed subgroup average is consistent.

Why Other Options Are Wrong:
Option 14 years would drag the overall average below 15. Option 14.75 years is too low to keep the overall average at 15 when combined with the other subgroups. Option 15 years would give a different total age, not matching 1200. Option “Cannot be determined” is incorrect because sufficient data are given to compute a unique answer.

Common Pitfalls:

• Using a simple average of 16 and 14 instead of applying correct weights based on group sizes.
• Forgetting that there are 40 remaining boys, not 80 or 60.
• Arithmetic errors while multiplying or subtracting totals.

Final Answer:
The average age of the remaining boys is 15.25 years.