In a public school, $\frac{1}{5}$ th of girls and $\frac{1}{4}$ th of boys are under 12 years of age. If the number of girls is $\frac{2}{5}$ th of the total, what part of the total strength of the school is accounted for by those who are 12 years or more of age?
(a)23\%
(b)45\%
(c)55\%
(d)77\%
Answer
Answer (as printed): D
Explanation
Let the total strength of the school be $x$. Number of girls $=\frac{2 x}{5}$; Number of boys $=\left(x-\frac{2 x}{5}\right)=\frac{3 x}{5}$. Number of students who are 12 years or more of age $$\begin{aligned} & =\left(1-\frac{1}{5}\right) \text { of } \frac{2 x}{5}+\left(1-\frac{1}{4}\right) \text { of } \frac{3 x}{5} \\ & =\left(\frac{4}{5} \times \frac{2 x}{5}\right)+\left(\frac{3}{4} \times \frac{3 x}{5}\right)=\frac{8 x}{25}+\frac{9 x}{20}=\frac{77 x}{100} . \end{aligned} \therefore \quad \text { Required percentage }=\left(\frac{77 x}{100} \times \frac{1}{x} \times 100\right) \%=77 \% .$$
Explanation as extracted from the printed page; notation may be imperfect.