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

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.