One-fifth of the light switches produced by a certain factory are defe

I guess there is somethings missing here "Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake"

There seems to be some missing data in the highlighted part.

assume 1000 produced

200 defective , 160 defective and rejected, 40 nondefective rejected by mistake

40 defective and not rejected , 760 non defective and not rejected, total non rejected and sold = 800

percent of the switches sold by the factory are defective = 40/800*100 = 5%

This may be a very stupid question but please help me understand how did we derive at(4/80)*100 ??

Is there a formula for this??

Option B --> 5 %

Just took 100 as the total number of switches and filled in numbers from there on.

Defective - 20 Non- Defective - 80
Rejected - 16 Rejected by mistake (1/20) - 4
Not rejected - 4 Net non-defective -- 80-4 = 76

# Sold but defective - 4
# sold - 76

--> 4/76 = ~5%


Thanks,
aimtoteach

Please give kudos if this helped!!

Similar question to practice: one-fifth-of-the-batteries-produced-by-an-upstart-factory-are-defectiv-189100.html

Thank you Bunuel - it was a good one indeed!!


Thanks,
aimtoteach

Hello!
Somehow, I am completely missing the caveat for this problem!

I am getting an answer of 25% which is clearly wrong!
What am I doing wrong? I have attached the chart I am working off of attached here.
Is it something to do with the 'mistakenly labeled rejected' bit?

So confused!

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

This made it easier for me.
.04/.8=.05=5%

When ever we find percent of something from something we usually do

The number/total number * 100

In the que we need to find % of no of defective swithches

No of defective switches sold from total switches is 4
And the total no of switches sold is 80

So we take 4/80 *100

Posted from my mobile device

Total number of bulbs = 500

We need to find
D -> defective ND -> Not defective
R-> rejected NR -> not rejected

----------D---------ND----------
R--------80---------20---------100
NR------20---------380--------400
---------100-------400---------500

To find 20/400 * 100

5%

We can let the total number of switches = n

So n/5 are defective and 4n/5 are not.

4/5 x n/5 = 4n/25 defective switches are rejected. Thus 1/5 x n/5 = n/25 defective switches are not rejected and are sold.

1/20 x 4n/5 = 4n/100 = n/25 non-defective switches are rejected by mistake.

Thus, a total of 5n/25 = n/5 switches are rejected. So a total of 4n/5 switches are not rejected and are sold.

So the percent of the switches sold that are defective is:

(n/25)/(4n/5) = 5n/(100n) = 1/20 = 5%

Answer: B

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

Given, Defective = T/5. So, Non-Defective = 4T/5

Let Total be T
Rejected Defective = (4/5) of Defective
So, Not Rejected Defective = (1/5) of Defective = (1/5)*(T/5) = T/25

Rejected Non-Defective = (1/20) of Non-Defective
So, Not Rejected Non-Defective = (19/20) of Non-Defective = (19/20)*(4T/5) = 19T/25

Given, all Not Rejected are sold.
So, Total sold = Not rejected defective + Not rejected non-defective = T/25 + 19T/25 = 20T/25

%of switches sold which are defective = (defective sold)/(total sold) = (not rejected defective) / (total not rejected) = (T/25)/(20T/25) * 100 = 5% (B)

Hi Scott, why can't the percentage be 4n/5/1*100= 80% ? Thanks in advance!

Only precaution in this question is to focus on last statement If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?


We have to divide by 0.8x not x

Let the total number of light switches be 100.

Total number of defective switches = (1/5)*100 = 20
Total number of non-defective switches = 80

Number of defective switches rejected = (4/5)*20 = 16
Number of non-defective switches rejected = 80*(1/20) = 4.
Thus, total number of sold switches = 100 - (16 + 4) = 80

Percentage of defective switches among sold = 4/80 = 5%.

Thus, the correct option is B.

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