hotel california

Anurag@Gurome wrote:

mirantdon 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?

Say, total number of lights in the hotel = 100
Also assume the number of lights that are supposed to be on = n.
Hence, number of lights that are supposed to be off = (100 - n)

Number of lights that are on = 80% of 100 = 80
Number of lights on that are supposed to be off = 40% of (100 - n) = 0.4(100 - n)
Number of lights off that are supposed to be on = 10% of n = 0.1n

Hence, total number of lights that are on = n - 0.1n + 0.4(100 - n) = 40 + 0.5n

Hence, (40 + 0.5n) = 80 => n = 80

Now, number of lights on that are supposed to be off = 0.4(100 - n) = 0.4(100 - 80) = 0.4*20 = 8

Hence, required percentage = (8/80)*100 = 10

The correct answer is D.

gmat1978 wrote:Can anyone please point out if anything is wrong in the following approach -

Let's say total number of lights = 100.
80% of lights are on in the evening = 80.
20% of the lights are off in the evening = 20.
Lights that are supposed to be off but are on = 40% of 20 = 8.
The percentage of lights that are on are supposed to be off = lights supposed to be off / lights that are on = 8/80 * 100 = 10%

Thanks