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.