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
(a)58\%
(b)67.5\%
(c)78\%
(d)82.5\%
Answer
Answer (as printed): C
Explanation
Let the number of boys and girls be $3 x$ and $2 x$ respectively. Then, $$\begin{aligned} & \text { No. of students who are not adults }=\left(\frac{80}{100} \times 3 x\right)+\left(\frac{75}{100} \times 2 x\right) \\ & \qquad=\left(\frac{12 x}{5}+\frac{3 x}{2}\right)=\frac{39 x}{10} . \\ & \begin{array}{r} \text { Required percentage }=\left(\frac{39 x}{10} \times \frac{1}{5 x} \times 100\right) \%=78 \% . \end{array} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.