Question

In an examination, out of 480 students, 85% of the girls and 70% of the boys passed. How many boys appeared in the examination if the total pass percentage was 75%?

• A. 370
• B. 340
• C. 320
• D. 360

Hint:

The overall pass rate is a weighted average of the boys' and girls' pass rates, so use alligation to split the total.

Answer 1

The Correct Option is C

Step 1: Set up the total number of passes.
Total students = 480. Total pass percentage = 75%, so students who passed = 75% of 480 = 360.

Step 2: Assume the number of boys.
Let the number of boys who appeared be \(x\). Then girls = \(480 - x\).

Step 3: Write the pass equation.
70% of boys plus 85% of girls equals the total passed: \[ \frac{70x}{100} + \frac{85(480-x)}{100} = 360 \]

Step 4: Solve for \(x\).
Multiply through by 100: \[ 70x + 85(480-x) = 36000 \] \[ 70x + 40800 - 85x = 36000 \] \[ -15x = -4800 \] \[ x = 320 \]

Step 5: Check the other options.
Option A (370) and B (340) do not balance the equation once you plug them back in, and option D (360) pushes the pass count past 360 when girls are added at 85%. Only \(x = 320\) fits exactly.

Final Answer:
The number of boys who appeared is 320. \[ \boxed{320} \]