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I would like to ask trivial question about calculating percents. Problem appeared during accounting calculations.

I've got $100$ Euro of Tax. There was a $10\%$ ratio which I was allowed to deduct from payments. Now there is a second pre-ratio, let's say $25\%$ which I must also calculate, ($25$ Euro) then I calculate old ratio from it. Result is $2.5$ Euro, which I can deduct.

I can write it down as $0.25 \cdot 100 \cdot 0.1 = 2.5$ and that looks pretty obvious.

What about rest of Tax which I must pay: How could I write it down using only multiplying/dividing? First thought about using $0.75 * 100 * 0.9$ is of course wrong.

I know I can get result from subtraction/addition, but what are fractions which I must use to get $97.5$ from multiplying?

N. F. Taussig
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Karol Nowak
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1 Answers1

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If you want to get 97,50 EUR proceed

100*(1-25%10%) = 100(1-0,25*0,10) = 100*(1-0, 025) = 100*0,975 = 97,50

If you can deduct two times (first time: 10%, second time: 25% of 10%), proceed

100*(1-10%-25%10%) = 100(1-0,10-0,25*0,10) = 100*(1—0,10-0, 025) = 100*(1—0,125) = 100*0,875 = 87,50

cgiovanardi
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  • So answer is i cannot make this calculations without subtracting/adding? Problem is not about how to calculate it but why I cannot do it in similarly fractions multiplying. – Karol Nowak Mar 09 '16 at 08:03
  • Speaking more general why do I must change type of mathematical operation? It seems intuitive that such calculations can be done using same type of operation. In other way: how to change this equation 100(1-0,10-0,25*0,10) to get 2.5 without change subtracting into multiplying. – Karol Nowak Mar 09 '16 at 08:35
  • My misconception occurred because I taught that calculating percent twice disallows to represent it as multiplication. It doesn't change anything. In first level I am also doing subtraction unconsciously to represent it as 100*(1-0.75). Thanks Jarek! – Karol Nowak Sep 29 '22 at 11:45