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I would like to aplly successively to reudction percentage to a price and I want to find the "global" reduction.

Apply a reduction of 19.6% and a 20% is different to apply a reduction of 39.6%.

So, i try to calculate the cumulative coefficient reduction $( 1 - 0.196) * ( 1 - 0.2 ) = 0.804 * 0.8 = 0.6432$

I thought it was a reduction of $(1 - 0.6432) * 100 = 35.68%$ ... but I think I do a mistake because

$(100 / 1.196) / 1.2 = 69.68$ And $100/1.3568 = 73.70$

So... what is a good way to calculate the global percentage of 2 successives reductions ?

Raphaël
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1 Answers1

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Your original calculation is correct: taking off $19.6$% and $20$% in succession is equivalent to taking off $35.68$% all at once. The other calculation doesn’t appear to have anything to do with the problem; there is certainly no reason to expect those two quantities to be equal (even after you correct $1.96$ to $1.196$).

For example, if you start with $100$, taking off $19.6$% leaves you with $80.4$; $20$% of $80.4$ is $16.08$, and $80.4-16.08=64.32$, which is indeed what’s left when you remove $35.68$% of $100$.

Brian M. Scott
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  • Ok, but how can I find a global percentage which gives me the same result $(Price - X%) - Y% = Price - Z% = New_Price$ ? I need this for a software when I can just apply "one reduction" and I have to apply "two reductions" – Raphaël Oct 08 '13 at 09:31
  • @Raphaël: That’s exactly what you did with your first calculation. For $X=19.6$ and $Y=20$, for instance, $Z=35.68$. In general if $x=X/100$ and $y=Y/100$, then $$Z=100\Big(1-(1-x)(1-y)\Big);,$$ just as you calculated $35.68$. – Brian M. Scott Oct 08 '13 at 09:44
  • But if I take an exemple. I apply my 35.68% reduction on 736.83. I do $736.83/1.3568 = 543.06$. If it works, I have to obtain the same result if I apply first the reduction of 19.6% then the reduction of 20%. $736.83/1.196 = 616.08 / 1.20 = 513.4$ ... There is something, somewhere I don't understand because 543.06 is different than 513.4 – Raphaël Oct 08 '13 at 10:01
  • @Raphaël: If you apply a $35.68$% reduction to $736.83$, you get $736.83-0.3568\cdot736.83=473.929056$. If you first apply $19.6$% reduction, you get $592.41132$, and when you apply a $20$% reduction to that you get $473.929056$, just as before. The calculations that you’re making are nonsensical: they have nothing to do with the problem, so there’s no reason to expect them to give equal results. – Brian M. Scott Oct 08 '13 at 10:04
  • I find my solution. I think I do a mistake in term I use. In fact I don't want to do a "reduction" but a "remove"...

    My OK calculation is Price / (1.196 x 1.20) ... and my "removal percentage" is in fact 43.52% and not 35.38%. $1.196x1.20 = 1.4352$

     – Raphaël Oct 08 '13 at 10:27
  • @Raphaël: My calculations are removing: one is removing $35.68$%, and the other is removing $19.6$% and then removing $20$% of what’s left. And they produce the same result. – Brian M. Scott Oct 08 '13 at 10:29
  • I think it's not the same in my mind. I think what you write is 100% correct and what I want is something weird that I can explain. But the fact is "I found my solution" with your help, even if it's not the same results XD. Thank you for your help – Raphaël Oct 08 '13 at 10:33
  • @Raphaël: Okay. :-) You’re welcome. – Brian M. Scott Oct 08 '13 at 10:36