Question

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? \[ \frac{3}{4} \times \text{Girls} = \frac{1}{2} \times \text{Boys} \]

• A. 852
• B. 720
• C. 568
• D. 284

Hint:

When dealing with word problems involving ratios and total quantities, express the variables and relationships algebraically, then solve step-by-step.

Answer 1

The Correct Option is A

Let the number of girls in the school be \( G \) and the number of boys be \( B \). The total number of pupils is \( G + B = 1420 \). From the given condition: \[ \frac{3}{4}G = \frac{1}{2}B \] Step 1: Multiply both sides of the equation by 4 to eliminate the fraction: \[ 3G = 2B \] Step 2: Express \( G \) in terms of \( B \): \[ G = \frac{2}{3}B \] Step 3: Substitute this into the total number of pupils equation: \[ \frac{2}{3}B + B = 1420 \] Step 4: Simplify the equation: \[ \frac{5}{3}B = 1420 \] Step 5: Multiply both sides by 3: \[ 5B = 4260 \] Step 6: Solve for \( B \): \[ B = \frac{4260}{5} = 852 \] Thus, the number of boys is 852.