In an exam of 480 students, 85% of the girls and 70% of the boys passed. If the overall pass percentage was 75%, how many boys appeared?

Introduction / Context:This problem requires forming an equation from group-wise pass rates and the overall pass rate, then solving for the unknown number of boys.

Given Data / Assumptions:

• Total students = 480.
• Pass rates: boys 70%, girls 85%.
• Overall pass % = 75%.
• Boys = B, girls = 480 − B.

Concept / Approach:Total passes = passes by boys + passes by girls. Equate this to 75% of 480 to solve for B.

Step-by-Step Solution:

Verification / Alternative check:Boys passed = 0.70 * 320 = 224; girls = 160, girls passed = 0.85 * 160 = 136; total passed = 360 = 75% of 480. Consistent.

Why Other Options Are Wrong:340, 360, 370 lead to totals not equal to 360 passes; 300 also fails the overall percentage.

Common Pitfalls:Mixing up which group has which rate, or using 75% of only boys or girls instead of the whole.

Final Answer:320