In a school, the ratio of boys to girls is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of the total students do not receive a scholarship?

Introduction / Context:This percentage-and-ratio question asks for the proportion of students who are not scholarship holders, given the gender ratio and the scholarship percentages for each group. The key is to use a convenient base matching the ratio, compute weighted adults (scholarship holders), then subtract from 100%.

Given Data / Assumptions:

• Boys : Girls = 3 : 2.
• 20% of boys get scholarships.
• 25% of girls get scholarships.
• All percentages are of their respective groups.

Concept / Approach:Work with a ratio base (e.g., 5k total students so that boys = 3k and girls = 2k). Compute scholarship holders in each group, sum them, convert to an overall percentage, and finally find the complement for non-scholarship students.

Step-by-Step Solution:

Verification / Alternative check:Pick actual numbers (boys 300, girls 200). Scholarship holders = 20% of 300 (60) + 25% of 200 (50) = 110 of 500 total ⇒ 22% scholarships → 78% not on scholarship.

Why Other Options Are Wrong:75% and 60% come from unweighted or incorrect averaging; 55% is far too low; 72% is a nearby distractor but not the computed complement of 22%.

Common Pitfalls:Simply averaging 20% and 25% without weighting by the 3 : 2 ratio gives the wrong total scholarship rate.

Final Answer:78%