In a certain school, the ratio of boys to girls is 7 : 5. If there are 2400 students in the school, then how many girls are there in the school?

Options

A. 500
B. 700
C. 800
D. 1000

Answer

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

### Step 1: Understand the ratio of boys to girls
The ratio of boys to girls is given as 7:5. This means that for every 7 boys, there are 5 girls.

### Step 2: Calculate the total parts in the ratio
To find the total number of parts represented by the ratio, we add the two parts together:
\[ 7 + 5 = 12 \]
So, the total parts in the ratio is 12.

### Step 3: Set up the equation for total students
Let \( X \) be the common multiplier for the ratio. The number of boys can be represented as \( 7X \) and the number of girls as \( 5X \). The total number of students in the school is given as 2400. Therefore, we can write the equation:
\[ 7X + 5X = 2400 \]

### Step 4: Simplify the equation
Combine the terms on the left side:
\[ 12X = 2400 \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides of the equation by 12:
\[ X = \frac{2400}{12} = 200 \]

### Step 6: Calculate the number of girls
Now that we have \( X \), we can find the number of girls using the ratio part for girls, which is \( 5X \):
\[ \text{Number of girls} = 5X = 5 \times 200 = 1000 \]

### Final Answer
Thus, the number of girls in the school is **1000**.

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