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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.
Solution
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.
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