Question

there are some students in two examination halls A and B. To make the numbers of student equal in each hall , 10 students were 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 student in B . find the number of students in each hall

Answer 1

Sol:
Consider the number of students in hall a = x

and number of students in hall b = y

When we send 10 students from hall a to b

Therefore, Number of students left in hall a = x - 10

and Number of students in hall b = y + 10

And, in this case number of student in each hall would be equal, so we obtain

x – 10 = y + 10

x – y = 20 ------------------(1) 

When we send 20 students are sent from b to a

Number of students in hall a = x + 20

and Number of students left in hall b = y - 20

In this case number of students in hall a becomes double the number of students in hall b,so we g obtain

x + 20 = 2( y – 20)

x + 20 = 2y – 40

x – 2y = -60 -----------------(2)

Solving  (1) from (2) we get

y = 80.

Substitute y in equation (1) we get x = 100

So that 100 students in hall a and 80 students in hall b.

Answer 2

no. of students in room B will be 80
and in roomA no. of students =100