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

 

  • Correct Answer
    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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