Question

School A has 30% more student than school B. if 120 more students join school B , The two schools will have the same number of students. what is the sum of the number of students in school A and school B initially ?

Answer 1

Let school A and B has x, and y number of students respectively.

Now,

According to the question,

$1$st condition: $x=30\%$ of $y+y$

$\Rightarrow x=\frac{30}{100}y+y$

$\Rightarrow x=\frac{3y}{10}+y$

$\Rightarrow x=\frac{3y+10y}{10}$

$\Rightarrow 10x=13y$

$\Rightarrow x=\frac{13y}{10}$ ……..$\left(1\right)$

$2$nd condition:

$\Rightarrow y+120=x$

$\Rightarrow x=y+120$

$\Rightarrow \frac{13y}{10}=y+120$ putting $\left(1\right)$

$\Rightarrow \frac{13y}{10}-y=120$

$\Rightarrow \frac{13y-10y}{10}=120$

$\Rightarrow 3y=1200$

$\Rightarrow y=400$

$\therefore x=\frac{13\times 400}{10}=520$

$\therefore$ Number of student in A school$=520$

Number of students in B school$=400$.