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# The output of a factory was increased by 10% to keep up with

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The output of a factory was increased by 10% to keep up with [#permalink]

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29 May 2006, 13:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the orginal output?

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29 May 2006, 15:21
The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the orginal output?

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Here is how I solved this.

Pick the output of the factory to be a number say 10

So,
(110/100)*10 = 11----after first 10% increase

(120/100)*11 = 66/5---after second 20% increase,

Let X be the decrease you would need to make.

(X/100)*(66/5) = 10

Solving this you should get X = approx 75%
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29 May 2006, 15:28
The book says the answer is 24% to RESTORE the original output. I don't know how to work this out.
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29 May 2006, 15:32
Actually...I think I got it after your post. Thanks.
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29 May 2006, 15:38
realist012 wrote:
The book says the answer is 24% to RESTORE the original output. I don't know how to work this out.

for example:
100
at 10% increase = 110
at 20% increase = 132

to bring back to 100=132-132*x
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29 May 2006, 17:58
i am getting 32 % and am doing 132-100/100....

I did not understand the explaination of 100=132 - 132 x.

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29 May 2006, 20:26
I think your approach is right akvenky, but it works out to be 32 is what percent of 132 not 100. I could be wrong though.

Anyone else?
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29 May 2006, 22:05
The approach should be this

Lets say the output was 100
First Increase, output is 110
Second increase, final output = 110 + 110*20/100 = 132

Let the decrease percent be X

Hence,
132 - 132*x/100 = 100
132*x/100 = 32
x = 800/33
~ 24%
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30 May 2006, 04:45
Let's assume Initial Output =100
After 1st increase, output = 110
After 2nd increase, output = 110 + 22 = 132

To bring it back to normal ouput, we have to bring the output to 100 which is 32 less than 132.

So the question - 32 is what percent of 132 gives an answer ~ 24%.
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30 May 2006, 10:50
Agree with 24%

Output 1 - x
Output 2 - 1.1x
Output 3 - 1.2 (1.1)x = 1.32x

To return to output one levels, we will have to subtract .032x from 1.32x. To calculate % decrease:

0.32x / 1.32x = .24 = 24%
30 May 2006, 10:50
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