# 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.

$\begin{array}{l}\text{Let the number of students in hall A be}\ x\ \text{and number of students in hall B be}\ y.\\ \text{If 10 students are send fro hall A to B, }\\ \text{Then the number of students in hall A will be lessened by 10 and that of B will be increased by 10.}\\ \text{The same will happen when 20 students are send from hall B to hall A.}\\ \text{Therefore, according to first case, we have}\\ x-10=y+10\\ x=y+20.....(1)\\ \text{By second case, we have}\\ x+20=2(y-20)\\ \Rightarrow\ y=80\\ \text{Putting }y=\text{80 in equation (1), we get}\\ x=80+20=100\\ \text{So, the number of students in hall A=100 and the number of students in hall B=80.}\end{array}$

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