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.

Answer 1

Given: Let the number of students in rooms A and B be x and y respectively.

Step-wise calculation:

1. After sending 10 from A to B they become equal:

x – 10 = y + 10

⇒ x – y = 20

2. After sending 20 from B to A, A has double B:

x + 20 = 2(y – 20)

⇒ x + 20 = 2y – 40

⇒ x – 2y = –60

3. Solve the system: From (1) x = y + 20.

Substitute into (2): (y + 20) – 2y = –60

–y + 20 = –60

–y = –80 

⇒ y = 80

Then x = y + 20

= 80 + 20

= 100

Room A has 100 students and Room B has 80 students.