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

1. ## 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

2. ## 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.

3. ## 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