# CAT Practice : Averages, Ratios, Mixtures

Averages

## Averages

Q.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?
1. 10 floors 50 rooms
2. 20 floors 20 rooms
3. 20 floors 25 rooms
4. 50 floors 10 rooms

Choice C. 20 floors 25 rooms

## Detailed Solution

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)

Correct Answer: 20 floors 25 rooms

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