Three - fourth of the number of girls in a school is equal to half of the number of boys .If the school has 1420 pupils ,how many of them are boys ?

Options

A. 852
B. 720
C. 568
D. 248

Answer

To solve the problem step-by-step, let's break it down:

### Step 1: Define Variables
Let the number of girls in the school be \( G \) and the number of boys be \( B \).

### Step 2: Set Up the Equation
According to the problem, three-fourths of the number of girls is equal to half of the number of boys. This can be expressed mathematically as:
\[ \frac{3}{4} G = \frac{1}{2} B \]

### Step 3: Rearrange the Equation
To eliminate the fractions, we can multiply both sides of the equation by 4:
\[ 3G = 2B \]
Now, we can express \( G \) in terms of \( B \):
\[ G = \frac{2}{3} B \]

### Step 4: Total Number of Pupils
The total number of pupils in the school is given as 1420. Therefore, we can write:
\[ G + B = 1420 \]

### Step 5: Substitute \( G \) in the Total Pupils Equation
Now, substitute \( G \) from the previous equation into the total pupils equation:
\[ \frac{2}{3} B + B = 1420 \]

### Step 6: Combine Like Terms
To combine the terms, we can express \( B \) in terms of a common denominator:
\[ \frac{2}{3} B + \frac{3}{3} B = 1420 \]
This simplifies to:
\[ \frac{5}{3} B = 1420 \]

### Step 7: Solve for \( B \)
To isolate \( B \), multiply both sides by \( \frac{3}{5} \):
\[ B = 1420 \times \frac{3}{5} \]
Calculating this gives:
\[ B = \frac{4260}{5} = 852 \]

### Step 8: Conclusion
Thus, the number of boys in the school is:
\[ \boxed{852} \]

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