Question

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination are 71, find the ratio of the number of boys to the number of girls.

Answer 1

Let the number of boys be x and the number of girls be y
$\text{Mean}=\frac{\text{sum of marks obtained by all}}{\text{total number of students}}$

For boys,
$70=\frac{\text{total marks obtained by boys}}{x}$

⇒ total marks obtained by boys = 70x

for girls,

$73=\frac{\text{total marks obtained by girls}}{y}$

⇒total marks obtained by girls = 73y

for whole class,

$71=\frac{\text{total marks obtained by all}}{x+y}$

⇒total marks obtained by all = 71(x +y)

$\Rightarrow 70x+73y=71x+71y\Rightarrow 71x-70x=73y-71y\Rightarrow x=2y\Rightarrow \frac{y}{x}=\frac{1}{2}\Rightarrow y:x=1:2$