# There are some students in the two examination halls A and B.

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,

then find the number of students in the both halls.

Solution:

Let the number of students in halls A and 8 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- 2 y) = 20+60 „  x-y-x + 2y~ 80 => y= 80

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

x – 80 = 20 => x = 100 and     y = 80

Hence, 100 students are in hall A and 80 students are in hall 8.