The average weight of girls is 15 and the average weight of boys is 30 and the average weight of the boys and the girls both is 25. If the number of boys are 12, then the number of girls is :

Options

A. 4
B. 6
C. 10
D. 18

Explanation

To solve the problem, we need to find the number of girls given the average weights of boys and girls, the average weight of both combined, and the number of boys.

### Step-by-Step Solution:

1. **Identify the given information:**
- Average weight of girls (G) = 15
- Average weight of boys (B) = 30
- Combined average weight of boys and girls (C) = 25
- Number of boys (nB) = 12

2. **Let the number of girls be nG.**

3. **Use the formula for combined average:**
The formula for the combined average is:
\[ C = \frac{(nB \times B) + (nG \times G)}{nB + nG} \]
Substituting the known values:
\[ 25 = \frac{(12 \times 30) + (nG \times 15)}{12 + nG} \]

4. **Calculate the total weight of boys:**
\[ 12 \times 30 = 360 \]

5. **Set up the equation:**
Substitute the total weight of boys into the equation:
\[ 25 = \frac{360 + (nG \times 15)}{12 + nG} \]

6. **Cross-multiply to eliminate the fraction:**
\[ 25(12 + nG) = 360 + 15nG \]

7. **Distribute 25:**
\[ 300 + 25nG = 360 + 15nG \]

8. **Rearrange the equation:**
Move all terms involving nG to one side:
\[ 25nG - 15nG = 360 - 300 \]
\[ 10nG = 60 \]

9. **Solve for nG:**
\[ nG = \frac{60}{10} = 6 \]

10. **Conclusion:**
The number of girls is **6**.