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Math Help - Calculating percentage 'uplift' by adding/subtracting to/from numerator/denominator

  1. #1
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    Calculating percentage 'uplift' by adding/subtracting to/from numerator/denominator

    Hi folks,

    I hope someone might be able to help me with this one. At work, we calculate a number of measures as simple percentages, and refer to 'uplift' as an amount of effort required to increase percentage by 1%.

    For example, if we achieved a target for 7500 out of 10000 items then we achieved 75%; to get to 76% we could do three things;
    1) add 100 to the numerator,
    2) subtract approx 132 from the denominator,
    3) add approx 417 to the numerator and denominator.

    The first value is straightforward, it's 1/10th of the denominator. I'd like to know how to calculate the amounts for options 2 and 3.

    Any help would be greatly appreciated.

    Scott
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  2. #2
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    Re: Calculating percentage 'uplift' by adding/subtracting to/from numerator/denominat

    for option 3:

    \frac{7500+x}{10000+x} = 0.76

    7500+x  = 0.76(10000+x)

    7500+x  = 7600 + 0.76x

    0.24x  = 100
    x = \frac{100}{0.24} \approx 416.7


    If you understand this, you can probably work out option 2 on your own.


    PS: Since you apepar to be asking for commercial purposes, i draw your attention to the disclaimer in my sig.
    Thanks from samtheskull
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  3. #3
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    Cool Re: Calculating percentage 'uplift' - generic formulae

    Hi,

    Many thanks for your speedy reply, I think I followed it ok;

    for option 2:

    \frac{7500}{10000-x} = 0.76

    7500  = 0.76(10000-x)

    7500  = 7600 - 0.76x

    7500 + 0.76x  = 7600

    0.76x  = 100

    x = \frac{100}{0.76} \approx 131.6

    Thanks, now I should be able to calculate the required effort for all three given scenarios for any size of items.


    Based on trying this for different numbers, I think the following is true for option 2:

    if \frac{a}{b} = c

    and \frac{a}{b-x} = c+0.01

    then x = \frac{\frac{b}{100}}{c+0.01}


    Based on trying your proof for different numbers, I think the following is true for option 3:

    if \frac{a}{b} = c

    and \frac{a+x}{b+x} = c+0.01

    then x = \frac{\frac{b}{100}}{1-(c+0.01)}


    and for option 1:

    if \frac{a}{b} = c

    and \frac{a+x}{b} = c+0.01

    then x = \frac{b}{100}



    Many thanks
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