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# 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 numbers of students would be in P and Q, respectively are

 A) 60, 40 B) 70, 50 C) 80, 60 D) 100, 80

 D) 100, 80

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,

$$\Large x + 20 = 2 \left(y - 20\right)$$

=> x + 20 = 2y - 40

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

On subtracting Eq. (ii) from Eq. (i), we get

-y + 2y = 20 + 60

=> y = 80

Putting the value of y in Eq. (i), we get

x - 80 = 20 => x =100

Hence, number of students in examination halls P and Q is 100 and 80, respectively.

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