The ratio of boys and girls in a school is 35:39. If the average of boys and girls in the school is 740, then the number of girls in the school is:

Options

A. 780
B. 740
C. 700
D. 720

Answer

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

1. **Understand the Ratio**: The ratio of boys to girls is given as 35:39. This means for every 35 boys, there are 39 girls.

2. **Let x be the Common Factor**: We can express the number of boys and girls in terms of a variable \( x \):
- Number of boys = \( 35x \)
- Number of girls = \( 39x \)

3. **Calculate the Total Number of Students**: The total number of students in the school is the sum of boys and girls:
\[ \text{Total students} = 35x + 39x = 74x \]

4. **Use the Average to Set Up an Equation**: We know that the average number of boys and girls is 740. The average can be calculated as:
\[ \text{Average} = \frac{\text{Total students}}{\text{Number of groups}} = \frac{74x}{2} \]
Setting this equal to the given average:
\[ \frac{74x}{2} = 740 \]

5. **Solve for x**: Multiply both sides by 2 to eliminate the fraction:
\[ 74x = 1480 \]
Now, divide both sides by 74:
\[ x = \frac{1480}{74} = 20 \]

6. **Find the Number of Girls**: Now that we have \( x \), we can find the number of girls:
\[ \text{Number of girls} = 39x = 39 \times 20 = 780 \]

Thus, the number of girls in the school is **780**.