In a room, there are some chairs and some people. If on each chair, only one person is seated, then there is no chair for exactly one person. If on each chair, two persons sit, then there is one vacant chair. What is the number of chairs in the room?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 3.
Let x be the number of chairs and y be the number of people.
If one person sits on each chair, there's one person without a chair. This means there's one more person than chairs.
So, y = x + 1 .....(1)
If two people sit on each chair, there's one chair vacant. This means there are two people for each chair, minus the vacant chair.
So, y = 2(x - 1) .....(2)
From equations (1) and (2),
x + 1 = 2x - 2
⇒ x = 3
Therefore, there are 3 chairs in the room.