percentages !

[neelgandham]

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?
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%

Source: A Friend
OA : After discussion

[Anurag@Gurome]

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?
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%

Source: A Friend
OA : After discussion

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.

[rijul007]

Total no of lights = 100
No of lights on = 80
No of lights supposed to be off = x
No of lights that are supposed to be off but are on = 4x/10

80 = 4x/10 + 9(100-x)/10
800 = 900-5x
5x = 100
x = 20
No of lights that are supposed to be off but are on = 4*20/10 = 8
No of the lights that are on are supposed to be off = 8/80 *100 = 10

Option D

[GMATGuruNY]

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?
A)22(2/9)%
B)16(2/3)%
C)11(1/9)%
D)10%
E)5%

Source: A Friend
OA : After discussion

This is a weighted average problem.

Let X = the lights that are supposed to be OFF.
Let Y = the lights that are supposed to be ON.
The total number of lights = X+Y = 100.

Percent of X that are actually on = 40.
Percent of Y that are actually on = 90. (Since 10% are off.)
Percent of X+Y that are actually on = 80.

X and Y are being combined to form a MIXTURE of X+Y.
To determine the ratio of X to Y in the mixture, we can use alligation, which dictates the following:

The proportion needed of each ingredient in the mixture is equal to the distance between the OTHER TWO PERCENTAGES.

Proportion needed of X = |90-80| = 10.
Proportion needed of Y = |40-80| = 40.
X:Y = 10:40 = 1:4.
Given 100 lights, since X:Y = 1:4 = 20:80, X=20 and Y=80.

Thus, the number of lights that are supposed to be OFF = 20.
Of these 20 lights, the number that are actually ON = .4(20) = 8.
Thus, (number of lights that are supposed to be OFF but are actually ON)/(total ON) = 8/80 = 10%.

The correct answer is D.