Question

There are some students in 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 two halls.

Answer 1

Let, the number of students in Hall A and B, be x and y respectively.
Then, according to the question,

x - 10 = y + 10........ (1)
y - 20 = (x + 20)/2 ....... (2)


from (1),

x = y + 20...... (3)

Now, putting the value of x from (3) to (2), we get,
y - 20 = (y + 20 + 20)/2
or, 2y - 40 = y + 40
or, y = 80...... (4)

Putting the value of y from (4) into (3)-
x = 80 + 20
or, x = 100

Therefore, there are 100 students in Hall A, and 80 students in Hall B.
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Answer 2

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

Now by given condition ,

x-10 = y+10

x-y = 20 ...........(1)

and

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

x-2y = -60 ............(2)

On subtracting Eq(2) from Eq (1),we get

(x-y) - (x-2y) = 20+60

x-y-x+2y = 80

y = 80

On putting y = 80 in Eq (1) , we get

x-80 = 20

x = 100

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