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?
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