There are two examination rooms A and B. If 10 candidates are sent fro

1.	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» Let the number of candidates in rooms A and B be ‘a’ and ‘b’ respectively. Given, If 10 candidates are sent from A to B, the number of students in each room is same. ⇒ a – 10 = b + 10 ⇒ a – b = 20 ----- (1) Also, If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. ⇒ a + 20 = 2(b – 20) ⇒ a – 2b = - 60 ------- (2) Subtracting equation 2 from equation 1 ⇒ a – b – a + 2b = 20 + 60 ⇒ b = 80 Thus, a = 80 + 20 = 100

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»

Let the number of candidates in rooms A and B be ‘a’ and ‘b’ respectively.

Given,

If 10 candidates are sent from A to B, the number of students in each room is same.

⇒ a – 10 = b + 10

⇒ a – b = 20 ----- (1)

Also,

If 20 candidates are sent from B to A, the number of students in A is double the number of students in B.

⇒ a + 20 = 2(b – 20)

⇒ a – 2b = - 60 ------- (2)

Subtracting equation 2 from equation 1

⇒ a – b – a + 2b = 20 + 60

⇒ b = 80

Thus, a = 80 + 20 = 100