help with percentage please

May 2010
2
0
I know this is a silly question but I'm not that good with maths so really need help.

I want to add 20% to a number but it doesn't add up right.

for example 20% taken from 1000 is 800 but if i wanted to put 20% back on 800 i always come up with 960.

I just want to make it up to 1000 again. It's because i have different figures i have taken 20% off but need then back to the original.

Sorry for being so thick (Thinking)
 

matheagle

MHF Hall of Honor
Feb 2009
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Most people don't know that if a stock goes down 50% then up 50% you're not back to where you started.
I'm not sure what your exact question is.
But if you decrease your initial amount by 20% you need to increase by 25% to get back to where you started.
 

Soroban

MHF Hall of Honor
May 2006
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Lexington, MA (USA)
Hello, shaun7996!

For example: 20% taken from 1000 is 800,
but if i wanted to put 20% back on 800, i always come up with 960.
. . Yes, this true.

I just want to make it up to 1000 again.
i have taken 20% off, but need then back to the original.

Scenario: Your boss asks you to take a 20% pay cut this month.
. . . . . . . He promises to give you a 20% raise next month,
. . . . . . . restoring your original salary.

Don't trust him!
He is either: (a) lousy at math, or (b) deliberately conning you.


You already did the math.

Your salary is $1000 per month.
With a 20% paycut, you'd get $800 this month.

Next month, he give you a 20% raise: .\(\displaystyle 20\% \times 800 \;=\;160\)

So your new salary is only: .\(\displaystyle \$800 + 160 \:=\:\$960\)

. . So he's wrong!


Why does this happen?

Consider what happens after your paycut.
(And ignore your original salary.)

You are now making $800 per month.

You want to make $1000 per month,
. . so you want a $200 raise.

What percent is that? . \(\displaystyle \frac{200}{800} \;=\;0.25 \;=\;{\color{blue}25\%}\)

See? .We can't use the same percent both ways.



There is a formula for this . . . if you want to memorize it.

If \(\displaystyle P\) is the percentage of paycut, to restore your salary,
. . your raise must be: .\(\displaystyle \frac{P}{1-P}\) percent.


Example: a 20% paycut.
To restore your salary, you need a: .\(\displaystyle \frac{0.20}{1-0.20} \:=\:\frac{0.20}{0.80} \;=\;0.25 \;=\;25\%\) raise.


Example: a 25% paycut.
You need a: .\(\displaystyle \frac{0.25}{1-0.25} \:=\:\frac{0.25}{0.75} \:=\:\frac{1}{3} \:=\:33\tfrac{1}{3}\%\) raise.



Take a more extreme case: your boss asks you to work at half-pay this month.
. . So you take 50% paycut.
To restore your salary, your boss must double your salary . . . a 100% raise.


Get the idea?

 
May 2010
2
0
yes i do and thanks alot for your detailed answer, very appreciated.
 

matheagle

MHF Hall of Honor
Feb 2009
2,763
1,146
And it doesn't matter which happens first.
If something increases by 25% and then decreases by 20%
you're back to where you started.
This always fools a lot of investors.
I've seen funds that jump 40 percent after they were down 80 percent.
They're still way way down.
That happened to a lot of funds after the Tech crash.
The Nasdaq is still down 60% from its high of 2001.
And lets not even go near the Nikkei.
That's way worse, and unfortunately where the US is heading. (Worried)