question_answer

The average of marks scored by the students of a class is 68. The average of marks of the girls in the class is 80 and that of boys is, 60. What is the percentage of boys in the class?

A) 40

B)  60

C)  65

D)  70

Correct Answer: B

Solution :

Let the number of boys and girls in the class be x and y, respectively. \[\therefore \]      \[60x+80y=68\,\,(x+y)\] \[\Rightarrow \]   \[60x+80y=68x+68y\] \[\Rightarrow \]   \[8x=12y\] \[\Rightarrow \]   \[2x=3y\]\[\Rightarrow \]\[y=\frac{2}{3}x\] \[\therefore \]Required percentage \[=\frac{x}{x+y}\times 100\] \[=\frac{x}{x+\frac{2}{3}x}\times 100=\frac{3x}{3x+2x}\times 100\] \[=\frac{3}{5}\times 100=60%\] Short Cut According to the question, Ratio of girls and boys = 8 : 12 = 2 : 3 \[\therefore \] Percentage of boys \[=\frac{3}{5}\times 100=60%\]