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.

Let the number of students in halls A and B are x and y, respectively.

Now, by given condition, x – 10 = y + 10

x - y = 20 …(i)

and (x + 20) = 2(y - 20)

x–2y = -60 …(ii)

On subtracting Eq. (ii) from Eq. (i), we get

(x - y) - (x -2y) = 80

y = 80

On putting y = 80 in Eq. (i), we get

x – 80 = 20

so, x = 100

Hence, 100 students are in hall A and 80 students are in hall B.

20