The average age of 30 girls is 13 years. The average age of the first 18 girls is 15 years. What is the average age of the remaining 12 girls?

Introduction / Context:
When averages of a whole group and a subgroup are given, the complementary subgroup’s average can be derived by working with totals (sum = average * count). This is a staple aptitude technique.

Given Data / Assumptions:

• Total girls = 30; average = 13 years.
• First 18 girls’ average = 15 years.
• Find average of remaining 12 girls.

Concept / Approach:
Let T be total age of 30 girls, T1 be total of first 18 girls, and T2 be total of the remaining 12. Then T = 30 * 13, T1 = 18 * 15, and T2 = T − T1. The required average = T2 / 12.

Step-by-Step Solution:

Verification / Alternative check:
The overall mean 13 lies between subgroup means 15 and 10, which is consistent with weighted averages (heavier weight on the 18 with mean 15 pulls the total above 11–12).

Why Other Options Are Wrong:

• 12yr, 16yr, 10.5 yr.: Do not match the derived total.
• None of these: Correct option exists (10yr).

Common Pitfalls:
Dividing 390 − 270 by 30 instead of 12, or averaging 13 and 15 directly without weights.

Final Answer:
10yr