Undoing Percentage ChangesDate: 07/10/2002 at 15:11:06 From: Elias Spielman Subject: Math percent equations If 10000 x 102% = 10200, then how do I figure the percentage to get back to my base number (10000), e.g., 10200 * 1.96% - 10200 = 10000.08? Date: 07/12/2002 at 17:54:39 From: Doctor Ian Subject: Re: Math percent equations Hi Elias, It's probably easier to see how this works if you use variables instead of numbers. If your original amount is A, and the percent increase is p, then the new amount is A' = A(1+p) You want to decrease it by some percentage q, to get back to A. That is, you want to find q such that A = A(1+p)(1-q) 1 = (1+p)(1-q) 1/(1+p) = 1 - q q = 1 - 1/(1+p) = (1 + p - 1)/(1+p) = p/(1+p) Let's check this with a simple example. If we increase something by 100%, we should have to decrease it by 50% to get back to where we started: q = 1.0 / 2.0 = 0.5 If we increase something by 1/3, we should have to decrease it by 1/4: q = (1/3) / (4/3) = 1/4 So this seems to work okay. So if p is 2 percent, q would be q = 0.02 / 1.02 Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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