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I need to reverse the effect of subtracting 4% from a large anmount of numbers.

One example: There was subtracted 4% from 100 making it 96. What kind of formula would make it 100 again?


Above is just an example. For the vast majority of the numbers I only know that 4% was subtracted. Something like this 100 - ((100 / 100) x 4))

Is it possible to do something like we do with Danish VAT:

  • Subtract 20% VAT: 100 x 0.80 = 80
  • Add the 25% VAT back: 80 x 1.25 = 100
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Divide by $0.96$... – draks ... Dec 3 '12 at 11:08
you mean "Substract 20% VAT"? – draks ... Dec 3 '12 at 11:43
Yes, my fault... – Cudos Dec 3 '12 at 11:50
Spelling hint: it's subtract; the only s there is the initial one. – Henning Makholm Dec 3 '12 at 11:58
up vote 4 down vote accepted

"$-4$%" means, that you have to multiply with $\frac{96}{100}$. To get the origininal value, you just have to multiply with $\frac{100}{96}$

Edit (Related to your update): It's exactly the same:

  • Subtract 20% VAT means, you have to multiply with $$\frac{100-\boldsymbol{20}}{100}=\frac{80}{100} = 0.8$$
  • to go back to the original value you have to multiply with $$\frac{100}{100-\boldsymbol{20}}=\frac{100}{80} = 1.25$$
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