Question

There are two examination rooms $A$ and $B$. If $10$ candidates are sent from $A$ to $B$, the number of students in each room is the same. If $20$ candidates are sent from $B$ to $A$, the number of students in $A$ is double the number of students in $B$. Find the number of students in each room.

Answer 1

Let the no: of students in rooms $A$ and $B$ be $x$ and $y$ respectively.

Then, $x-10=y+10$

$\Rightarrow x-y=20⟶\left(i\right)$

and $x+20=2(y-20)$

$\Rightarrow x-2y=-60⟶\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$ simultaneously,we get ,

$x=100$ & $y=80$

$\therefore$ The no: of students in room $A$ is $100$ & in room $B$ is $80$.