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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
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B
20
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C
80
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D
60
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Solution

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

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