varun289 wrote:80% of the lights in a hotel were on at 8.00 pm on some evening. If 40% of lights that were expected to be off, were in fact on, and 10% of lights that were expected to be on, were in fact off; what percent of the lights that are on, are the lights that were not expected to be on?
A. 10
B. 12
C. 100/9
D. 8
E. 18
We can treat this as a MIXTURE PROBLEM.
Let X = the bulbs that SHOULD BE OFF and Y = the bulbs that SHOULD BE ON.
X: Of these bulbs, the PERCENTAGE ON = 40%.
Y: Of these bulbs, the PERCENTAGE ON = 90%. (Since 10% are off.)
X+Y: Of ALL the bulbs, the PERCENTAGE ON = 80%.
Use
alligation.
Step 1: Plot the 3 percentages on a number line, with the two starting percentages (40% and 90%) on the ends and the mixture percentage (80%) in the middle.
X (40%)----------------------80%----------(90%) Y
Step 2: Calculate the distances between the percentages.
X (40%)--------
40----------80%----
10---(90%) Y
Step 3: Determine the ratio in the mixture.
The ratio of X to Y in the mixture is equal to the RECIPROCAL of the distances in red:
X:Y = 10:40 = 20:80.
Thus, if the total number of bulbs = 100:
X=20 and Y=80.
40% of the X-bulbs are on = .4(20) = 8.
80% of the total bulbs are on = .8(100) = 80.
(X-bulbs on)/(total bulbs on) = 8/80 = 1/10 = 10%.
The correct answer is
A.
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