Boys and girls in a college are in the ratio 3 : 2. If 20% of the boys and 25% of the girls are adults, what percentage of the total students are not adults?

Introduction / Context:
This problem blends ratios with basic percentage calculations. We are given the gender composition of a college and the fraction of adult students within each gender, and we must find the overall percentage of students who are not adults. This is typical of demographic or survey-style aptitude questions where careful aggregation is key.

Given Data / Assumptions:

• Boys : Girls = 3 : 2.
• Adults among boys = 20% of boys.
• Adults among girls = 25% of girls.
• Assume a convenient total matching the ratio (e.g., 5k students) to simplify arithmetic; results are ratio-invariant.

Concept / Approach:
Use a ratio base to avoid cumbersome algebra. With 3 parts boys and 2 parts girls, compute adult counts in each group using the given percentages. Sum adult counts to get total adults. Then convert to a percentage of the whole. The non-adult percentage is 100% minus the adult percentage.

Step-by-Step Solution:

Verification / Alternative check:
Pick actual numbers: if total is 500, boys = 300, girls = 200. Adults = 20% of 300 (60) + 25% of 200 (50) = 110 adults. Adult % = 110/500 = 22%; non-adults = 78%.

Why Other Options Are Wrong:
58%, 67.5%, and 82.5% arise from mixing or averaging percentages incorrectly. 72% is an arbitrary nearby value but does not match the computed adult complement of 22%.

Common Pitfalls:
Directly averaging 20% and 25% without weighting by the 3 : 2 ratio, or subtracting the wrong quantity from 100%. Weighted aggregation is essential.

Final Answer:
78%