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Math Help - Reverse percentages

  1. #1
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    Question Reverse percentages

    I don't know if this is the correct place for this question but here goes. This might be a very obvious question but if for example I have a wage of 23000 after paying tax at 25%, what is the gross pay? I thought that if I did 25%x = 23000, then x would equal 23000/0.25 but that give a ludicrous figure of 92000. So obviously that isn't correct. What is the correct method?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Reverse percentages

    If the tax rate is r%, your gross pay (before tax) is P, and your net pay after tax N, then the formula to remember is:

    N = P(1-r).

    For example if your gross pay is 10000, and tax is 25%. then your net pay is 10000(1-.25) = 7500.

    Now let's turn it around. You can rearrange the above formula to get P by itself:

    P = N/(1-r)

    So - if net pay is 23000, tax rate is 25%, then gross pay is 23000/(1-.25) = 23000/0.75 = 30667.
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  3. #3
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    Re: Reverse percentages

    Thank you very much for that. It has alway perplexed me.

    Cheers

    Brian
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