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There are some students in the two exami...

There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students 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, then find the number of students in the both halls.

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Let the number of students in halls A and B are x and y, respectively.
Now, by given condition, `" " x-10=y+10`
`rArr " " x-y=20 " " ...(i)`
and `" " (x+20)=2(y-20)`
`rArr " " x-2y=-60 " " ...(ii)`
On subtracting Eq. (ii) from Eq. (i) , we get
`(x-y)-(x-2y)=20+60`
`x-y-x+2y=80 rArr y = 80`
On putting y = 80 in Eq. (i), we get
x-80=20`rArr`x=100
and `" "`y=80
Hence, 100 students are in hall A and 80 students are in hall B.
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