One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

### 3 Responses to “Light Switches”

Ivan says:

Easy Problem if you know fractions and use a piece of scrap paper.

1/5L are defective so –> 4/5L are not defective

4/5 of 1/5L means 4/25L are defective & rejected so –> 1/5 of 1/5L means 1/25L are defective & NOT rejected.

1/20 of 4/5L (remember 4/5L is not defective) means 4/100L are NOT defective BUT rejected by mistake so –> 19/20 of 4/5L ( These are NOT defective and NOT rejected) means 76/100L.

ALL switches NOT rejected are sold so we add 76/100L (NOT defective & NOT rejected) + 1/25L (Defective BUT NOT rejected). We have to have common denominators to add fractions so 1/25L converts to 4/100L + 76/100L = 78/100L are the TOTAL switches sold!!

We are done yet though!! We have to find what percent of the switches sold are defective so we have to find out what % of 78 is 4?? Remember the last equation 4/100L + 76/100L = 78/100L

4/78 reduces to 2/39 and 2 is roughly 5% of 39 because it is exactly 5% of 40 so the answer is B!!

Baron says:

I have a question. how can 4/100 +76/100 = 78/100? According to my math, I thought that 4/100 + 76/100 = 80/100?

Nina says:

You could simply take a real value for the number of products produced from the factory as being 100.

1/5*100=20 defective
4/5*20=16 rejected

100-20=80 non-defective
1/20*80=4 rejected by mistake

So, if 80-4=76 not rejected of the non-defective and 20-16=4 not rejected of the defective. If we total these values we have 80. If we look back at the value of the defective switches that were not rejected that totals 4. To find out the percentage of defective switches that were sold would be simply 4/80 or 1/20=.05 or 5%