The boys and girls in a college are in the ratio $3 : 2$. If $20\%$ of the boys and $25\%$ of the girls are adults, the percentage of students who are not adults is

### Concept & Strategy When given a ratio and percentages, always assign concrete values to the ratio parts (like $300$ and $200$) instead of working with abstract variables like $3x$ and $2x$. Furthermore, calculate the target value directly: if you need the percentage of *non-adults*, apply the complement percentages ($100\% - \text{adult}\%$) directly to the bases. ### Step-by-Step Solution * **Given:** Ratio of Boys : Girls = $3 : 2$. Adult boys = $20\%$. Adult girls = $25\%$. * **Calculation / Deduction:** Let the number of boys be $300$ and the number of girls be $200$. Total number of students = $300 + 200 = 500$. Find the percentage of non-adults for each group: Non-adult boys = $100\% - 20\% = 80\%$. Non-adult girls = $100\% - 25\% = 75\%$. Calculate the actual number of non-adults: Number of non-adult boys = $80\%$ of $300 = \frac{80}{100} \times 300 = 240$. Number of non-adult girls = $75\%$ of $200 = \frac{75}{100} \times 200 = 150$. Total number of non-adults = $240 + 150 = 390$. Calculate the overall percentage: Percentage of non-adults = $\left( \frac{390}{500} \right) \times 100\%$ $= \frac{390}{5} = 78\%$. ### Exam Strategy & Shortcut Use weighted averages for an even faster solution. The percentage of adults is a weighted mix of the two groups: $\text{Overall Adult } \% = \frac{(3 \times 20\%) + (2 \times 25\%)}{3 + 2} = \frac{60 + 50}{5} = \frac{110}{5} = 22\%$. If $22\%$ of the total population are adults, then the non-adults are $100\% - 22\% = 78\%$. This requires virtually zero scratchpad math. ### Common Pitfall A frequent trap is calculating the adult populations first ($60$ and $50$), and then calculating that percentage ($22\%$), and mistakenly selecting a corresponding option if available, forgetting the question asked for students who are **not** adults. Always highlight the final requirement. ### Final Answer **Therefore, the correct answer is 78%.**