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

Options

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

Answer

To solve the problem step by step, we start by analyzing the given information:

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

2. **Letting Variables Represent the Numbers**: We can let the number of boys be \( 35x \) and the number of girls be \( 39x \), where \( x \) is a common multiplier.

3. **Finding the Total Number of Students**: The total number of students (boys + girls) can be expressed as:
\[ \text{Total students} = 35x + 39x = 74x \]

4. **Using the Average**: We know the average number of boys and girls is 740. The average is calculated as:
\[ \text{Average} = \frac{\text{Total number of students}}{\text{Number of groups}} = \frac{(35x + 39x)}{2} = \frac{74x}{2} = 37x \]
Given that this average is equal to 740, we can set up the equation:
\[ 37x = 740 \]

5. **Solving for \( x \)**: To find \( x \), we divide both sides of the equation by 37:
\[ x = \frac{740}{37} = 20 \]

6. **Finding the Number of Boys**: Now that we have \( x \), we can find the number of boys:
\[ \text{Number of boys} = 35x = 35 \times 20 = 700 \]

Thus, the number of boys in the school is **700**.