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Thread: Percentage Confusion

  1. #1
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    Percentage Confusion

    Hi,


    Today at work I was trying to understand whether a given amount (revenue) is with or without VAT. (vat is 21%).


    Here is the amount with VAT (1980.50)
    Here is the amount without VAT (1636.4)


    The way I've taught myself to add or subtract a percentage from an amount is to either multiply by 1.21 to add 21% or to multiply by 0.79 to subtract 21%.


    Here is what confused me today.
    If i do this calculation to add 21% to 1636.4 (1636.4 * 1.21), i get 1980.044 (this is correct)
    If i do this calculation to subtract 21% from 1980.5 (1980.5 * 0.79) I get 1564.6 (expected to 1636.4)


    Why am I not getting 1636.4 when i subtract 21% from 1980.5?


    Also. i was told by my colleague to subtract 21% from 1980.5 I am supposed to divide by 1.21. This way the
    calculation makes sense (1980.5 / 1.21 = 1636.77).


    Why my colleague's way works and why mine does not?


    Thanks in advance for your help!
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  2. #2
    Junior Member Cervesa's Avatar
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    Re: Percentage Confusion

    Here is the amount with VAT (1980.50)
    Here is the amount without VAT (1636.4)
    If $A$ is the amount w/o VAT, then $A(1.21) = \text{ the amount with VAT}$

    since $A(1.21) = \text{ amount with VAT}$, then $A = \dfrac{\text{amount with VAT}}{1.21}$
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  3. #3
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    Re: Percentage Confusion

    Quote Originally Posted by Cervesa View Post
    If $A$ is the amount w/o VAT, then $A(1.21) = \text{ the amount with VAT}$

    since $A(1.21) = \text{ amount with VAT}$, then $A = \dfrac{\text{amount with VAT}}{1.21}$
    Thank you for trying to help me with my poor math skills.

    What you said is the correct way to calculate an amount with/without VAT. What i want to know is how and why the formula works (specifically for calculating an amount without VAT)? If VAT is 21%, then why not just the amount with VAT * 0.79 to subtract 21%? I dont want to just remember a formula without understanding how it works.
    Last edited by dani0157; Feb 9th 2019 at 11:06 AM.
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  4. #4
    Junior Member Cervesa's Avatar
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    Re: Percentage Confusion

    It's a common misconception that a fixed percentage increase followed by the same percentage decrease gets one back to the original value.

    To make things simple, consider the original amount to be 100. A 21% increase of the value 100 would yield the value 121 ok with that?

    Following that increase with a 21% decrease on the new value of 121 will not yield the original value of 100.

    The reasoning is that the follow on decrease of 21% is based on the already increased value of 121, not 100. 21% of 121 is 25.41

    (.79)(121) = 95.59 = 121 - 25.41

    In plain language, 21% of 121 is greater than 21% of 100, hence the decrease is greater than the initial increase.

    Hope this clears it up for you.
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