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# How percentages balance out in multiplications

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Intern
Joined: 17 Aug 2016
Posts: 48
How percentages balance out in multiplications  [#permalink]

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21 Mar 2017, 14:19
Hi guys, this is a little tip that I had in my mind and I would like to ask you if you can clarify me how percentages balance out in a multiplication.

The question may be really silly, so I apologise from the beginning.

I had the trip while playing around with some revenue problems. How come if I want to keep the revenue stable, to a 25% increase in the volume I only need a 20% decrease in price?

More in general, how come in a multiplication if a factor increases by x% the other needs to decrease only by y% - with y<x - to maintain the product equal?

Could anyone give me any insight on that?
Intern
Joined: 18 Aug 2014
Posts: 49
Location: India
GMAT 1: 740 Q49 V40
GPA: 3.11
Re: How percentages balance out in multiplications  [#permalink]

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22 Mar 2017, 09:32
Suppose you are increasing 100 by 20% (X%) then 100 will become 120, an increase of 20 points. In this case if we want to decrease the value to 100, we need to remove 20 points from the original value. ie remove Y%(which is equal to 20) from 120

(Y*120)/100 = 20
Y=20*100/120 = 16.66%

here Y<x because 20 is a smaller part of 120 when compared to 100.
the simple logic here is ,If we are increasing on value in a product you have to decrease the other value proportionally to make the result constant.

I exam you can use this tip:
1) If one factor of a product is increased by X% then the other factor should be decreased by (X/100+X)*100 %. It means when one factor of a product is increased by (N/D) then the other factor is decreased by (N/N+D)
2) If one factor of a product is decreased by X% then the other factor should be increased by (X/100-X)*100 %. It means when one factor of a product is decreased by (N/D) then the other factor is increased by (N/N-D)
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Intern
Joined: 17 Aug 2016
Posts: 48
Re: How percentages balance out in multiplications  [#permalink]

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25 Mar 2017, 04:48
AARONRAMSEY wrote:
Suppose you are increasing 100 by 20% (X%) then 100 will become 120, an increase of 20 points. In this case if we want to decrease the value to 100, we need to remove 20 points from the original value. ie remove Y%(which is equal to 20) from 120

(Y*120)/100 = 20
Y=20*100/120 = 16.66%

here Y<x because 20 is a smaller part of 120 when compared to 100.
the simple logic here is ,If we are increasing on value in a product you have to decrease the other value proportionally to make the result constant.

I exam you can use this tip:
1) If one factor of a product is increased by X% then the other factor should be decreased by (X/100+X)*100 %. It means when one factor of a product is increased by (N/D) then the other factor is decreased by (N/N+D)
2) If one factor of a product is decreased by X% then the other factor should be increased by (X/100-X)*100 %. It means when one factor of a product is decreased by (N/D) then the other factor is increased by (N/N-D)

Hi AARONRAMSEY - thanks for the post. To me, while the example of 100 increased by 20% and then decreased by 16% to go back to 100 is pretty intuitive, the case of the product remains a bit counter intuitive. I will play a bit with the formulas you shared in the second part of the post - using some real example - to try to grasp this topic a bit better. Thanks for the insight!
Re: How percentages balance out in multiplications &nbs [#permalink] 25 Mar 2017, 04:48
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