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One night a certain hotel rented 3/4 of its rooms. including

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One night a certain hotel rented 3/4 of its rooms. including [#permalink] New post 27 Sep 2010, 23:01
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46% (02:55) correct 54% (01:35) wrong based on 142 sessions
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80
[Reveal] Spoiler: OA
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Re: OG 10 Q 248 - % rented [#permalink] New post 27 Sep 2010, 23:09
Expert's post
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20
33 1/3
35
40
80

please explain the logic


Consider total # of rooms to be 100;
As 3/5 of the rooms are air conditioned then # of rooms that are air conditioned is 3/5*100=60;

3/4 rooms were rented --> 1/4*100=25 were NOT rented;
2/3 of air conditioned rooms were rented --> 1/3*60=20 air conditioned room were NOT rented;

20/25=4/5=80%.

Answer: E.
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Re: OG 10 Q 248 - % rented [#permalink] New post 27 Sep 2010, 23:13
This can be easily solved using the matrix method
as the % is asked i can choose a good # for total rooms..let me choose 60 as all the 3 fractions given have 3,4&5 in the denominator and 60 is divisible by all thease 3 #s.

Given:
Total Rented=(60)3/4 = 45
Total AC rooms = (60)3/5 = 36
Total AC rooms rented = (36)2/3 = 24

Plug in:

Rented Not-rented |
|
AC 24 12 | 36
|
|
Non AC |
...............................................................
45 15 | 60


qtn is what % is 12 in 15 = 1200/15 = 80%
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Re: OG 10 Q 248 - % rented [#permalink] New post 28 Sep 2010, 19:48
conditined un condition total

rented 24 21 45

not rent 12 3 15

total 36 24 60

total rooms 60
total rented 60*3/4 =45
total conditioned 60*3/5 =36
total conditioned 36*2/3 24
1200/15=80% (rooms that were not rented were air conditioned
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Re: OG 10 Q 248 - % rented [#permalink] New post 28 Sep 2010, 19:56
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The problem will be very easy to solve if you take a 2x2 matrix and work with the given data.

Given fractions - 2/3, 3/4, 3/5 -- L.C.M - 60 [consider this to be the total number of rooms.]





Rooms
RentedAvailableTotal
AirCon24 (Given 2/3 of total aircon)1236 (Given - 3/5 of total)
NonAircon21324
Total45 (Given - 3/4 of total)1560 (Total considered)


Hence % of non-rented (available) that were aircon -- 12/15 -- 4/5 -- 80% (E).
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Re: rooms in hotel [#permalink] New post 05 Mar 2011, 11:54
Rooms Rented: 3/4
Rooms Not Rented: 1/4

Total AC: 3/5
AC Rented: (2/3)*(3/5) = 2/5
AC Not rented: 3/5 - 2/5 = 1/5.

% of AC that is yet to be rented per total of not rented room;

((1/5)/(1/4))*100 = (4/5)*100 = 80% of remaining(non-rented) rooms are AC.

Ans: "E"
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Re: rooms in hotel [#permalink] New post 05 Mar 2011, 11:59
Let's consider T as the total number of rooms.
If 2/3 of the air conditioned rooms were rented, than 1/3 of them were not rented. We know that the total number of air-conditioned rooms is 3/5, thus we can say that 1/5 of the total rooms in the hotel were air-conditioned and not rented (1/3 x 3/5 = 1/5). (a)

We know that 3/4 of the total rooms were rented, thus 1/4 were not rented. (b)

Using (a) and (b), we can calculate the ratio of air-conditioned rooms to the non-rented rooms: (1/5 x T) / (1/4 x T) = 4/5, and thus non air-conditioned rooms make 80% of the total non-rented rooms.
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Re: OG 10 Q 248 - % rented [#permalink] New post 03 Nov 2011, 02:17
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20
33 1/3
35
40
80

please explain the logic



Can someone please explain where am i going wrong here?

Let total rooms be 60

Rented rooms = 3/4 * 60 = 45

Rented AC rooms = 2/3 * 45 = 30

Total AC rooms = 3/5* 60 = 36


% Rooms that are AC and not rented = [(36 - 30) /36] * 100 = 16 * (2/3)


I am not sure where is my mistake... Can someone please correct me ??? :? :? :?
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Re: One night a certain hotel rented 3/4 of its rooms. including [#permalink] New post 11 Aug 2014, 18:42
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Re: One night a certain hotel rented 3/4 of its rooms. including [#permalink] New post 11 Aug 2014, 20:14
Expert's post
siddhans wrote:
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20
33 1/3
35
40
80

please explain the logic



Can someone please explain where am i going wrong here?

Let total rooms be 60

Rented rooms = 3/4 * 60 = 45

Rented AC rooms = 2/3 * 45 = 30

Total AC rooms = 3/5* 60 = 36


% Rooms that are AC and not rented = [(36 - 30) /36] * 100 = 16 * (2/3)


I am not sure where is my mistake... Can someone please correct me ??? :? :? :?


"including 2/3rd of their air conditioned rooms" implies that 2/3rd of their air conditioned rooms were a part of the rented rooms.

So if total air conditioned rooms = 36 (as found by you above), 2/3rd of these i.e. 24 of these were rented. So 12 AC rooms were rented.

Total number of rooms that were not rented = 60 - 45 = 15

So AC rooms form what percent of rooms not rented? 12/15 * 100 = 80%
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Re: One night a certain hotel rented 3/4 of its rooms. including [#permalink] New post 11 Aug 2014, 23:59
Refer diagram below (Solved using matrix method)
Going as per serial no (Marked in red) in the matrix

1. Let the total no of rooms = 100

2. 75% rented = 75

3. Not rented = 100-75 = 25

4. \frac{3}{5} th of 100 are air conditioned = \frac{3}{5} * 100 = 60

5. \frac{2}{3} rd of air conditioned rooms are AC= \frac{2}{3} * 60 = 40

6. Not Rented AC rooms = 60-40 = 20

Percentage of Not rented AC rooms = \frac{20}{25}* 100 = 80%

Answer = E
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Re: One night a certain hotel rented 3/4 of its rooms. including   [#permalink] 11 Aug 2014, 23:59
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