Question

In a school there are only two sections A and B if 10 students are sent from A to B the no of students in each room is same if 20 students are sent from B to A the no of students in A is double the number of students in B find the no of students in each room

Answer 1

Consider the number of students in a = x, b = y.
When we send 10 students from hall a to b,
a = x - 10
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 20 students are sent from b to a,
a = x + 20
b = y - 20
In this case number of students in hall a becomes double the number of students in hall b,
so we obtain,
x + 20 = 2( y – 20)
x + 20 = 2y – 40
x – 2y = -60 -------- (2)
Solving (1) from (2)
x – y = 20
x – 2y = -60
we get y = 80.
Substitute y in equation (1)
x - 80 = 20
we get x = 100
So that 100 students in hall a and 80 students in hall b.