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 becomes the same. If 20 students are sent from B to A, the number of students in room A becomes the double of the number of students in room B. Find the number of students in each room.​

Answer 1

Answer:

30 students in both rooms

Answer 2

Answer:

Let the number of students in classroom A be x

Let the number of students in classroom B be y.

If 10 students are transferred from A to B, then we have:

x – 10 = y + 10

⇒x – y = 20 …..(i)

If 20 students are transferred from B to A, then we have:

2(y – 20) = x + 20

⇒2y – 40 = x + 20

⇒ -x + 2y = 60 …..(ii)

On adding (i) and (ii), we get:

y = (20 + 60) = 80

On substituting y = 80 in (i),

we get:

x – 80 = 20

⇒x = (20 + 80) = 100

Hence, the number of students in classroom A is 100

and

the number of students in classroom B is 80