Question

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. Find the number of students in the two halls.

Answer 1

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 equation (ii) from equation (i), we get

(x – y) – (x – 2y) = 20 + 60

x – y – x + 2y = 80

⇒ y = 80

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

x – 80 = 20

⇒ x = 100

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