In a school 900 students, the average age of the boys is 13 years and that of the girls is 9 years. If the average age of the school is 10 years, then the number of girls in the school is

Solution: Let us assume, no.of  boys are ‘x’,  no.of  girls are ‘y’.

$\therefore x+y=900\to \left(1\right)$

Age of  the boys = 13x

$\therefore Averageoftheschool\Rightarrow 10$

$\frac{13x+9y}{x+y}=10\Rightarrow 13x+9y=10x+10y$

$\Rightarrow 13x-10x=10y-9y$

$y=3x\to \left(2\right)$

$\left(1\right)\&\left(2\right)$

$x+3x=900\Rightarrow 4x=900\Rightarrow x=225$

$\therefore Boys=225$

$girls=900-225=675girls$