# 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

**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 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.

**Solution:**

Let us take the A examination room will be x and the B examination room will be y

If 10 candidates are sent from A to B, the number of students in each room is same. According to the above condition equation will be

$y+10=x-10$

$0=x-y-10-10$

$x-y-20=0 \cdots(i)$

If 20 candidates are sent from B to A, the number of students in A is double the number of students in B, then equation will be

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

$x+20=2 y-40$

$x+20-2 y+40=0$

$x-2 y+20+40=0$

$x-2 y+60=0 \cdots(i i)$

By subtracting the equation $(i)$ from $(i i)$ we get, $y=80$

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

Hence 100 candidates are in A examination Room,

80 candidates are in B examination Room.