The Principle Behind Percentage Increase/Decrease Question

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asker

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Hello,

I'm trying to understand the principle behind why a decrease from .17 to .11 = 35% but an increase from .11 to .17 = 54%. Shouldn't they be the same? Why can't you calculate it either way and have it be the same? [Unless I am doing the math completely wrong.]

Thank you!
 
asker said:
I'm trying to understand the principle behind why a decrease from .17 to .11 = 35% but an increase from .11 to .17 = 54%. Shouldn't they be the same?
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Why would they be the same?!? :shock:

In the first case, you are starting with 0.17 and working with 0.06 of that (in particular, you are subtracting, but that's irrelevant). That's a hair over one-third of your starting amount.

In the second case, you are starting with 0.11 and working with 0.06 of that (in particular, you are adding, but that's irrelevant). That's more than half of your starting amount.

Why would six-of-seventeen be the same as six-of-eleven? Do you think that 1/3 and 1/2 are pretty much the same value?
 
Thank you very much!

I have been staring at this and trying different things and I am seeing what you are saying. Like if something went from .25 to .50 the price has doubled 100%? But if it went from .50 to .25 it would be half at 50%. Correct me if I am wrong. I am closing in on it somewhat. Different calculators seem to give opposite negative number signs which confuses things also.

Thank you.
 

Your boss asks you to take a cut in salary during a bad time for the company.
She promises to restore your salary after the crisis.

This is her deal:
You accept a 10% reduction in salary,
then she will give you a 10% raise.
Fair?

Suppose you earn $1,000 per week.

A 10% cut means: \(\displaystyle 10\% \times 1000 = \$100\text{ less.}\)
Your reduced salary will be: \(\displaystyle \$1,000 - 100 \,=\,\$900\text{ per week.}\)

Then you get a 10% raise.
\(\displaystyle 10\% \times \$900 \,=\, \$90\)
Your 'restored' salary will be: \(\displaystyle \$900 + 90 \,=\,\$990.\)
. . You just lost $100!

You see, that is what happens when the percent decrease
. . and the percent increase are equal.


 
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