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There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is the same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

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Hint- Assume the number of students in respective rooms to be two different variables, and compute them.

Let, the number of students in room A and B are x and y respectively.
Then it is given if 10 candidates are sent from A to B, the number of students in each room is the same.
Thus $x - 10 = y + 10$
$ \Rightarrow x - y = 20$…………………. (1)
Now it is also given that if 20 candidates are sent from B to A, the number of students in A is double the number of students in B
$x + 20 = 2\left( {y - 20} \right)$
$ \Rightarrow x - 2y = - 60$………………………….. (2)
Now let’s solve equation (1) and equation (2)
$ \Rightarrow x - y = 20$……………………… (1)
$ \Rightarrow x - 2y = - 60$…………………. (2)
Now in equation (1) multiply by 2 on both side, we get
$ \Rightarrow 2x - 2y = 40$………………. (3)
Subtract equation (3) and equation (2)
$2x - 2y - x + 2y = 40 + 60$
$ \Rightarrow x = 100$
Now substitute the value of x in equation (1) we get
$
  100 - y = 20 \\
   \Rightarrow y = 80 \\
 $
The number of students in room A is 100 and the number of students in room B is 80.

Note- In such types of questions, just focus on how many numbers (as in this question there are given numbers of students) are shifted where, according to them, make equations and solve them to obtain the variables. This will give the correct answer.
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