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
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.
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.
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