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 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.

Given:

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 same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B.

To do:

We have to find the number of students in each room.

Solution: Let the number of students in room A and the number of students in room B be $x$ and $y$ respectively.

If 10 candidates are sent from A to B, the number of students in each room is same.

This implies,

$x-10=y+10$

$x=y+10+10$

$x=y+20$.....(i)

If 20 candidates are sent from B to A, the number of students in A is double the number of students in B.

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

$x + 20 = 2y-40$

$y+20+20=2y-40$ (From (i))

$2y-y=40+40$

$y=80$

Substituting $y=80$ in equation (i), we get,

$x=80+20$

$x=100$

Therefore, the number of students in room A is 100 and the number of students in room B is 80.

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