The boys and girls in a school are in the the ration `9 : 5`. If the number of girls is `320`, then the total strength of the school is

Options

A. `840`
B. `896`
C. `920`
D. `576`

Answer

To solve the problem, we need to find the total strength of the school given the ratio of boys to girls and the number of girls.

### Step-by-step Solution:

1. **Understand the Ratio**: The ratio of boys to girls is given as 9:5. This means for every 9 boys, there are 5 girls.

2. **Identify the Number of Girls**: We are told that the number of girls is 320.

3. **Set Up the Ratio**: Let the number of boys be represented as \( B \) and the number of girls as \( G \). According to the ratio:
\[ \frac{B}{G} = \frac{9}{5} \]

4. **Substitute the Number of Girls**: Since \( G = 320 \), we can substitute this value into the ratio:
\[ \frac{B}{320} = \frac{9}{5} \]

5. **Cross-Multiply to Solve for Boys**: Cross-multiplying gives us:
\[ 5B = 9 \times 320 \]

6. **Calculate \( 9 \times 320 \)**:
\[ 9 \times 320 = 2880 \]
So, we have:
\[ 5B = 2880 \]

7. **Divide by 5 to Find the Number of Boys**:
\[ B = \frac{2880}{5} = 576 \]

8. **Find the Total Strength of the School**: The total strength of the school is the sum of the number of boys and girls:
\[ \text{Total Strength} = B + G = 576 + 320 \]

9. **Calculate the Total Strength**:
\[ \text{Total Strength} = 896 \]

### Final Answer:
The total strength of the school is **896**.

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