The average age of 120 members of a society is 60.7 years. After 30 new members join, the average age of all 150 members becomes 56.3 years. What is the average age of the 30 newly joined members?

Introduction / Context:
This question focuses on how the average of a group changes when new members join. It uses the idea of total sums behind averages and asks you to deduce the average of the newly added members from the change in overall average. This is a common pattern in quantitative aptitude tests involving populations, salaries or age distributions.

Given Data / Assumptions:

• Original number of members = 120.
• Original average age = 60.7 years.
• New members added = 30.
• Total members after addition = 150.
• New average age = 56.3 years.
• We assume only the new members changed the composition.

Concept / Approach:
The average age multiplied by the number of members gives the total age. We first compute the total age of the original 120 members. Then we compute the total age of all 150 members after the new members join. The difference between these totals is the combined age of the 30 new members, and dividing by 30 gives their average age.

Step-by-Step Solution:
Step 1: Original total age = 120 * 60.7 = 7284 years.Step 2: New total age after all 150 members = 150 * 56.3 = 8445 years.Step 3: Combined age of 30 new members = 8445 − 7284 = 1161 years.Step 4: Average age of the 30 new members = 1161 / 30.Step 5: 1161 / 30 = 38.7 years.

Verification / Alternative check:
We can reason qualitatively: the overall average age decreased when new members joined, which implies that their average age must be lower than 60.7. The calculated value 38.7 is indeed lower. If we reconstruct the total using 30 members of average age 38.7 and 120 members maintaining their original total, we obtain 8445 total age and 56.3 average again, confirming the calculation.

Why Other Options Are Wrong:
An average such as 36.5 or 37.2 would not reduce the total age enough to bring the overall average down to 56.3. A value like 38.3 would be close but not exact and would slightly change the final average. A value like 39.5 would not reduce the overall average sufficiently. Only 38.7 makes both totals consistent.

Common Pitfalls:

• Not converting averages into totals before subtracting.
• Attempting to use simple differences between averages without considering group sizes.
• Arithmetic mistakes when multiplying decimals by large numbers.

Final Answer:
The average age of the newly joined 30 members is 38.7 years.