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

Try this with the alligation (weighted average) idea instead of an equation. The overall pass rate of 75% sits between the boys' rate of 70% and the girls' rate of 85%.

1. Find the gap on each side: girls' rate is 10 points above the average (85 minus 75), and boys' rate is 5 points below the average (75 minus 70).
2. Apply the alligation rule: the ratio of boys to girls is the inverse of these gaps, so boys : girls = 10 : 5 = 2 : 1.
3. Split the total: total students = 480, split in ratio 2 : 1 means boys get \( \frac{2}{3} \) of 480.

So boys = \( \frac{2}{3} \times 480 = 320 \). This matches option C, so 320 boys appeared.

Let's summarize:

• Alligation works because the overall percentage is a weighted average of two groups, so the group ratio equals the inverse of the distance from that average.

This route skips the algebra and reaches 320 in three quick lines.