The average age of 30 girls is 13 yr. The average of first 18 girls is 15 yr. Find out the average age of remaining 12 girls.

Options

A. 12yr
B. 10yr
C. 16yr
D. 10.5yr

Answer

To solve the problem step by step, we will follow these calculations:

1. **Understand the given information**:
- The average age of 30 girls is 13 years.
- The average age of the first 18 girls is 15 years.
- We need to find the average age of the remaining 12 girls.

2. **Calculate the total age of all 30 girls**:
- The formula for average is:
\[ \text{Average} = \frac{\text{Total Age}}{\text{Number of Girls}} \]
- Rearranging gives us:
\[ \text{Total Age} = \text{Average} \times \text{Number of Girls} \]
- For 30 girls:
\[ \text{Total Age of 30 girls} = 13 \times 30 = 390 \text{ years} \]

3. **Calculate the total age of the first 18 girls**:
- Using the same formula:
- For the first 18 girls:
\[ \text{Total Age of first 18 girls} = 15 \times 18 = 270 \text{ years} \]

4. **Calculate the total age of the remaining 12 girls**:
- The total age of the remaining 12 girls can be found by subtracting the total age of the first 18 girls from the total age of all 30 girls:
\[ \text{Total Age of remaining 12 girls} = \text{Total Age of 30 girls} - \text{Total Age of first 18 girls} \]
- Substituting the values:
\[ \text{Total Age of remaining 12 girls} = 390 - 270 = 120 \text{ years} \]

5. **Calculate the average age of the remaining 12 girls**:
- Now, we can find the average age of the remaining 12 girls using the average formula:
\[ \text{Average Age of remaining 12 girls} = \frac{\text{Total Age of remaining 12 girls}}{\text{Number of remaining girls}} \]
- Substituting the values:
\[ \text{Average Age of remaining 12 girls} = \frac{120}{12} = 10 \text{ years} \]

Thus, the average age of the remaining 12 girls is **10 years**.