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Math Help - help with percentage please

  1. #1
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    help with percentage please

    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
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  2. #2
    MHF Contributor matheagle's Avatar
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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.
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  3. #3
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    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: . 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.
    (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? . \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.
    To restore your salary, your boss must double your salary . . . a 100% raise.


    Get the idea?

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  4. #4
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    yes i do and thanks alot for your detailed answer, very appreciated.
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  5. #5
    MHF Contributor matheagle's Avatar
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    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.
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