# CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

###### CAT Questions | Averages | Averages - Rooms

The question is from CAT Ratio, Mixtures and Averages. It is all about how do we form the equation and solve it to get the answer. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2020.

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?

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

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##### Method of solving this CAT Question from Ratio, Mixtures and Averages: How the individual data points affect the average?

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?"

##### Hence, the answer is "20 floors 25 rooms".

Choice C is the correct answer.

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