The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively.

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 is 71, find the ratio of the number of boys to the number of girls.

Solution:

Let the number of girls be x and the number of boys be y.

Mean marks of boys $=\frac{\text { sum of marks obtained by boys }}{\text { Total }}$

$\Rightarrow 70=\frac{\text { sum of marks obtained by boys }}{y}$

$\Rightarrow 70 y=$ sum of marks obtained by boys $\ldots(1)$

Mean marks of girls $=\frac{\text { sum of marks obtained by girls }}{\text { Total number of girls }}$

$\Rightarrow 73=\frac{\text { sum of marks obtained by girls }}{x}$

$\Rightarrow 73 x=$ sum of marks obtained by girls

Mean marks of all the students $=\frac{\text { sum of marks obtained by all }}{\text { Total number of students }}$

$\Rightarrow 71=\frac{\text { sum of marks obtained by boys and girls }}{x+y}$

$\Rightarrow 71(x+y)=70 y+73 x$              (from (1) and (2))

$\Rightarrow 71 x+71 y=70 y+73 x$

$\Rightarrow 71 y-70 y=73 x-71 x$

$\Rightarrow y=2 x$

$\Rightarrow \frac{y}{x}=\frac{2}{1}$

Hence, the ratio of the number of boys to the number of girls is 2:1.

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