Question

There are two classrooms A and B. If 10 students 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 A becomes double the number of students in B. Find the number of students in each room.

Answer 1

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)

y = 80

On substituting y = 80 in (i), we get:

x – 80 = 20

⇒ x = (20 + 80)

⇒ x = 100

Hence, the number of students in classroom A is 100 and the number of students in classroom B is 80.