There are 500 rooms in a multi-floored hotel. However, due to a change

Question

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%. What was the original number of rooms per floor in the hotel?

A. 50 rooms
B. 40 rooms
C. 25 rooms
D. 20 rooms
E. 10 rooms

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hinasingh · Answer

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%. What was the original number of rooms per floor in the hotel?

Let x be the original number of rooms per floor in the hotel.
then number of floors = 500/x
After rule change, number of floors = 500/x - 5 and number of rooms in each floor = x + 5. the total number of rooms decrease by 10% => 500 - 0.1*500 = 450.
(x+5)*(500/x - 5) = 450 
solving for x we get, x = 25.
Answer C

hloonker · Answer

Sorry i got the wrong answer (d).

I let x be the original number of rooms per floor in the hotel.
then number of floors = 500/x

After rule change, i set the equation as (x-5)* ((500/x) + 5) = 450. Isn't this right? the original number of rooms per floor +5 more rooms. and you multiply by (x-5) the new number of floors. that's what will equal 450?

GMATking94 · Answer

The number of floors comes out to be 20. But the question asks what was the original number of rooms per floor. So we need to divide 500 by 20. So ans is 25.

just to explain further, if we consider x as the number of floors we can write the eq as

(450/x-5)-(500/x)=5,

Now solving x in this quadratic eq,
(x-20)(x+25)=0, hence x=20. floors.

Let me know if this is clear now.

bumpbot · Answer

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There are 500 rooms in a multi-floored hotel. However, due to a change

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There are 500 rooms in a multi-floored hotel. However, due to a change

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