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

$\begin {array} {1 1} (A)\;40 & \quad (B)\;20 \\ (C)\;80 & \quad (D)\;60 \end {array}$

Let the number of boys and girls be $x$ and $y$
$\therefore 52x+42y=50(x+y)$
$52x+42y=50x+50y$
$52x-50x=50y-42y$
$2x=8y$
$x = 4y$
Total number of students in the class = $x+y$
$= 4y+y$
$= 5y$
Percentage of boys = $\large\frac{4\not{y}}{\not{5}\not{y}} \times {\not100}^{20}$
$= 80$
Ans : (C)