There are two examination halls P and Q. If 10 students shifted P to Q, then the number of students will be equal in both the examination halls. If 20 students shifted from Q to P, then the students of P would be doubled to the students of Q. The number of students would be in P and Q respectively are?

Let number of students in examination halls P and Q is x and y, respectively
Then as per the first condition,
x - 10 = y + 10
⇒ x - y = 20 ..............(i)
As per the second condition,
⇒ x + 20 = 2( y - 20)
⇒ x - 2y = - 60 ...............(ii)
On subtraction Eq. (ii) from Eq. (i), we get
- y + 2y = 20 + 60
⇒ y = 80
Putting the value of y Eq. (i) we get,
x - 80= 20 ⇒ x = 100
Hence, number of students in examination halls P and Q is 100 and 80, respectively.