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

Introduction / Context:
This is a classic weighted average question involving an existing group and a group of new members. The overall average age drops after new members join, so the new members must be younger on average than the original members. The task is to compute that new average.

Given Data / Assumptions:
- Original number of members = 120. - Original average age = 60.7 years. - New members joining = 30. - New average age of all 150 members = 56.3 years. - We must find the average age of the 30 new members.

Concept / Approach:
The total age of the original group is original average multiplied by 120. The new total age after addition is new average multiplied by 150. The difference between these totals is exactly the combined age of the 30 new members. Dividing that difference by 30 gives the required average age for the newcomers.

Step-by-Step Solution:
Step 1: Original total age = 120 * 60.7 = 7284 years. Step 2: New total number of members = 120 + 30 = 150. Step 3: New total age = 150 * 56.3 = 8445 years. Step 4: Total age of new members = new total age minus original total age. Step 5: So, age of new members = 8445 - 7284 = 1161 years. Step 6: Number of new members = 30. Step 7: Average age of new members = 1161 / 30 = 38.7 years.

Verification / Alternative check:
Check the direction of change. Original average was 60.7; after adding members with average 38.7, overall average falls to 56.3, which lies between 38.7 and 60.7 and is closer to 60.7 because there are more original members. This confirms that the computed value is reasonable and consistent with average behaviour.

Why Other Options Are Wrong:
- 36.5, 37.2 and 38.3 would lead to a different combined total and not give an overall average of 56.3. - 40.1 is too high and would not reduce the average as much as required by the question.

Common Pitfalls:
Learners sometimes average 60.7 and 56.3 directly or forget to multiply by the number of members. Another mistake is to divide the change in average by the change in count without using totals. Always go back to total age = average * number of members for each group and then compare.

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