The average weight of girls is 15 and the average weight of boys is 30 and the average weight of boys and 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

Answer

To solve the problem step by step, we will use the method of alligation.

### Step 1: Identify the averages
- Average weight of girls (G) = 15
- Average weight of boys (B) = 30
- Average weight of both boys and girls (A) = 25

### Step 2: Set up the alligation
We will use the alligation formula to find the ratio of the number of girls to the number of boys. The formula for alligation is:

\[ \text{Difference between boys' average and overall average} : \text{Difference between girls' average and overall average} \]

### Step 3: Calculate the differences
- Difference between boys' average and overall average:
\[ B - A = 30 - 25 = 5 \]

- Difference between girls' average and overall average:
\[ A - G = 25 - 15 = 10 \]

### Step 4: Write the ratio
Now we can write the ratio of the number of girls (G) to the number of boys (B):
\[ \text{Ratio of girls to boys} = \frac{10}{5} = 2:1 \]

### Step 5: Relate the ratio to the number of boys
Let the number of girls be \(2x\) and the number of boys be \(x\). We know that the number of boys is given as 12:
\[ x = 12 \]

### Step 6: Calculate the number of girls
Now, substituting \(x\) back into the equation for the number of girls:
\[ \text{Number of girls} = 2x = 2 \times 6 = 12 \]

### Final Answer
Thus, the number of girls is **12**.