Question

The average score of boys in an examination of a school is 71 and that of girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls that appeared in the examination.

Answer 1

Let the number of boys = x
Average score of boys = 71
Total score of boys = 71x
Let the number of girls = y
Average score of girls = 73
Total score of girls = 73 y
According to the question,

$Averagescore=\frac{Totalaverage}{Totalnumberofstudents}$

$\Rightarrow 71.8=\frac{71x+73y}{x+y}$

$\Rightarrow 71.8x+71.8y=71x+73y\Rightarrow 0.8x=1.2y$

$\Rightarrow \frac{x}{y}=\frac{1.2}{0.8}=\frac{3}{2}$

Hence, the ratio of the number of boys to the number of girls = 3 : 2.