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# Eighty percent of the lights at Hotel California are on at 8

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Director
Joined: 23 Sep 2007
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Eighty percent of the lights at Hotel California are on at 8 [#permalink]

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25 Jun 2008, 23:24
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Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
22(2/9)%
16(2/3)%
11(1/9)%
10%
5%

Please resfrain from posting solutions from the source.
Manager
Joined: 24 Apr 2008
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Re: PS Hotel lights [#permalink]

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25 Jun 2008, 23:54
Let F be the lights that are supposed to be off and N be lights supposed to be ON

Now .4F+.9N=.8(N+F)
=> 4F=N

We need to find: 0.4F / .8(N+F) x100 = 10%
Director
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Re: PS Hotel lights [#permalink]

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26 Jun 2008, 00:04
Nice solution, the best and shortest one yet.
Director
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Re: PS Hotel lights [#permalink]

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26 Jun 2008, 00:08
gmatnub wrote:
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?
22(2/9)%
16(2/3)%
11(1/9)%
10%
5%

Please resfrain from posting solutions from the source.

Let X be lights that should be ON,
Let Y be lights that should be OFF

Lights that are ON = [X - 0.1X] + 0.4[Y] = 0.8[Total]
=> 0.9X+ O.4Y = 0.8[X+Y]
=> 0.1 X = 0.4 Y

Its given in Q that "forty percent of the lights that are supposed to be off are actually on"

i.e 0.1 X = 0.4 Y => 0.1 = 0.4Y/X , thus 10%
Re: PS Hotel lights   [#permalink] 26 Jun 2008, 00:08
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# Eighty percent of the lights at Hotel California are on at 8

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