Question

The average marks of boys in a class is $52$ and the girls is $42$ . The average marks of boys and girls combined is $50$ . The percentage of boys in the class is

• A. $0$
• B. $20$
• C. $80$
• D. $60$

Answer 1

The correct option is C $80$

$LetBoy:Girl=x:y$
$M_{avg}=\frac{Mb\left(x\right)+Mg\left(y\right)}{x+y}$
$\Rightarrow 50=\frac{52x+42y}{x+y}$
$\Rightarrow 50x+50y=52x+42y$
$\Rightarrow 2x=8y$
$\Rightarrow \frac{x}{y}=4..........\left(i\right)$

$=\frac{x}{x+\frac{x}{4}}\times 100\left(from\left(i\right)\right)$
$=\frac{x}{\frac{5x}{4}}\times 100$
$=\frac{4}{5}\times 100$
$=80$