Average age drop after intake: An adult class has average age 40 years. When 12 new students with average age 32 join, the class average falls by 4 years to 36. What was the original class strength?

Introduction / Context:
Average changes due to new members can be modeled with totals before and after. The new group average after addition lets us solve for the original size via algebra.

Given Data / Assumptions:

• Original average = 40 years
• 12 join with average = 32 years
• New average = 36 years

Concept / Approach:
Let original size be n. Original total = 40n. New total = 40n + 12 * 32. New count = n + 12. Set new average to 36 and solve for n.

Step-by-Step Solution:

Verification / Alternative check:
Original total 40 * 12 = 480. After adding 12 at 32, add 384 to get 864. New count 24. 864 / 24 = 36, correct.

Why Other Options Are Wrong:

• 10, 11, 15, 18: do not satisfy the average equation.

Common Pitfalls:
Using 32 percent rather than 32 years, or neglecting that both numerator and denominator change when new members join.

Final Answer:
12