The average marks of boys in a class is 40 and that of girls is 45 . The average marks of both boys and…
The average marks of boys in a class is 40 and that of girls is 45 . The average marks of both boys and girls combined is 42 . Then the percentage of boys in the class is
\(60 \%\)
\(30 \%\)
\(40 \%\)
\(50 \%\)
Solution
Let the number of boys and girls in the class are \(m\) and \(n\) respectively, so according to given informations,
Total marks of boys \(=40 \mathrm{~m}\)
and total marks of girls \(=45 n\)
and total marks of boys and girls \(=42(m+n)\)
\(\begin{array}{ll}
\therefore & 40 m+45 n=42(m+n) \\
\Rightarrow & 2 m=3 n \Rightarrow \frac{m}{3}=\frac{n}{2}=\lambda \quad \text{(let)} \\
\therefore & m=3 \lambda \text { and } n=2 \lambda
\end{array}\)
So, the percentage of boys in the class is
\(\begin{aligned}
& \frac{m}{m+n} \times 100 \\
& =\frac{3 \lambda}{3 \lambda+2 \lambda} \times 100=\frac{3}{5} \times 100=60 \% \\
\end{aligned}\)
Hence, option (a) is correct.