Question

Question 19
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.

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
$\Rightarrow$ x – y = 20
and (x + 20) = 2 (y – 20)
$\Rightarrow$ x – 2y = - 60
On subtracting Eq. (ii) from Eq. (i), we get
(x – y) - (x- 2y) = 20 + 60
x – y – x + 2y = 80 $\Rightarrow$ y = 80
on putting y = 80 in Eq. (i), we get
(x – y) – (x – 2y) = 20 + 60
x – y – x + 2y $\Rightarrow$ x = 100
and y = 80
hence, 100 students are in hall A and 80 students are in hall B.