Question

There are some students in 2 examination halls - A , B. In order to make the students equal in each room, 20 are sent from A to B. But 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 the TWO halls.

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Answer 1

Let there be x and y no. of students originally in A and B resp.

then acc to first condition

$x - 20 = y + 20 \\ = > x - y = 40 \\ = > x = y + 40..........(1)$

now as per 2nd condition

$x + 20 = 2(y - 20) \\ = > x + 20 = 2y - 40 \\ = > y + 40 + 20 = 2y - 40.....from(1) \\ = > y - 2y = - 40 - 60 \\ = > - y = - 100 \\ = > y = 100 \\ \\put \: y = 100 \: in \: (1) \\ we \: get \: x = 140$

which gives us 140 students in A and 100 in B.

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