• May 16th 2010, 06:07 AM
shaun7996
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)
• May 16th 2010, 06:54 AM
matheagle
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.
• May 16th 2010, 07:08 AM
Soroban
Hello, shaun7996!

Quote:

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.

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

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

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

. . So he's wrong!

Why does this happen?

Consider what happens after your paycut.

You are now making $800 per month. You want to make$1000 per month,
. . so you want a \$200 raise.

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

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

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

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

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

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

Take a more extreme case: your boss asks you to work at half-pay this month.
. . So you take 50% paycut.

Get the idea?

• May 16th 2010, 07:36 AM
shaun7996
yes i do and thanks alot for your detailed answer, very appreciated.
• May 16th 2010, 08:26 AM
matheagle
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)