# 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 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 eq2 from eq1

a – b – a + 2b = 20 + 60

b = 80

Thus, a = 80 + 20 = 100

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