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

Solution

## The correct option is C $$80$$  $$Let\,Boy:Girl=x:y$$  $$M_{avg}^{{}}=\frac{Mb\left( x \right)+Mg\left( y \right)}{x+y}$$  $$\Rightarrow 50=\frac{52x+42y}{x+y}$$  $$\Rightarrow 50x+50y=52x+42y$$  $$\Rightarrow 2x=8y$$  $$\Rightarrow \frac{x}{y}=4\,\,\,\,\,\,\,\,..........\left( i \right)$$  $$%boy=\frac{x}{x+y}\times 100$$  $$\,\,\,\,\,\,\,\,\,\,\,\,\,=\frac{x}{x+\frac{x}{4}}\times 100\,\,\,\,\,\,\,\left( from\left( i \right) \right)$$  $$\,\,\,\,\,\,\,\,\,\,\,\,\,=\frac{x}{\frac{5x}{4}}\times 100$$  $$\,\,\,\,\,\,\,\,\,\,\,=\frac{4}{5}\times 100$$  $$\,\,\,\,\,\,\,\,\,\,=80%$$ Maths

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