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Question 42: There are 500 rooms in a multi-floored hotel. However, due to a change in rule, the hotel has to decrease the number of floors by 5. However, the management is able to put 5 more rooms in each floor. Over all, the number of rooms in the hotel decreases by 10%. Find the number of floors and the number of rooms/floor the hotel originally had?
Let the number of floors be x and rooms per floor be y
So, xy = 500
After the change,
(x-5) * (y+5) = 450
xy – 5y + 5x – 25 = 450
500 – 5(y-x) – 25 = 450 (As, xy = 500)
5(y-x) = 25
y-x = 5 (Only option c satisfies the above condition)
The question is "Find the number of floors and the number of rooms/floor the hotel originally had?"
Choice C is the correct answer.
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