If 75% of students in a school are boys and the number of girls is 310, the number of boys is

Options

A. 910
B. 920
C. 930
D. none of these

Answer

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

### Step 1: Understand the percentage of boys and girls
We know that 75% of the students are boys. Therefore, the remaining percentage of students, which is 100% - 75%, will be girls.

**Hint:** Remember that the total percentage must always equal 100%.

### Step 2: Calculate the percentage of girls
From the above calculation, we find that:
- Percentage of girls = 100% - 75% = 25%

**Hint:** Always subtract the percentage of one group from 100% to find the percentage of the other group.

### Step 3: Set up the equation
We know that 25% of the total number of students is equal to the number of girls, which is given as 310. We can express this mathematically:
- Let the total number of students be \( x \).
- Therefore, \( 25\% \) of \( x \) = 310.

**Hint:** Use the formula for percentage: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \).

### Step 4: Convert the percentage to a fraction
We can express 25% as a fraction:
- \( 25\% = \frac{25}{100} = \frac{1}{4} \)

**Hint:** Converting percentages to fractions can simplify calculations.

### Step 5: Set up the equation with the fraction
Now we can write the equation:
- \( \frac{1}{4} x = 310 \)

**Hint:** Isolate \( x \) by multiplying both sides of the equation by 4.

### Step 6: Solve for \( x \)
Multiply both sides by 4:
- \( x = 310 \times 4 \)
- \( x = 1240 \)

**Hint:** Make sure to perform the multiplication carefully to avoid errors.

### Step 7: Calculate the number of boys
Now that we have the total number of students, we can find the number of boys:
- Since 75% of the students are boys, we calculate:
- Number of boys = \( 75\% \) of \( 1240 \)
- Number of boys = \( \frac{75}{100} \times 1240 = \frac{3}{4} \times 1240 \)

**Hint:** You can simplify the calculation by multiplying directly or using the fraction.

### Step 8: Perform the calculation
Calculating the number of boys:
- Number of boys = \( 930 \)

**Hint:** Double-check your calculations to ensure accuracy.

### Final Answer
The number of boys in the school is **930**.