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

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. Find the number of students in the two halls.

A: 100 students in hall A,80 students in hall B

B: 200 students in hall A, 45 students in hall B

C: 80 students in hall A, 70 students in hall B

D: 120 students in hall A, 60 students in hall B

Explanation:

Let the number of students in hall A be x,

and, the number of students in hall B be y,

Now, the number of students send from A to B is 10,

So, the equation formed will be,

X – 10 = y + 10 x = 20 + y ... (i)

Now, the number of students send from B to A is 20, which is double the number previously sent from A to B. So, the equation will be,

x + 20 = 2 (y – 20)

x + 20 = 2y – 40

x – 2y = - 60 ... (ii)

Putting the value of (i) in eqn ( ii)

20 + y – 2y = - 60 y = 80 Substituting this value on eqn (i) to find the value of x,

x = 20 + 80 = 100

:. The number of students in hall A = 100

The number of students in hall B = 80