[Math] How to handle the following percentage scenarios

arithmeticfinance

I have the following scenarios, but I am unclear on how to handle them correctly. I start off with a value like 200 and the following scenarios are:

  1. Remove 10% from 200, and then remove a compound 20% from that value.

  2. Remove 10% from 200, and then remove 20% from 200. I guess this is just like removing 30%, correct?

  3. Add 10% to 200, and then remove a compound 20% from that value.

  4. Add 10% to 200, and then remove 20% from 200.

I am also unclear on on a certain on something else because I have been given 2 different answers. If I take 100 and want to remove 10%, is it:

100 * 0.9 = 90

or

100 / 1.1 = 90.9090….

What is the difference above?

Lastly, is there a formula than can be converted into an algorithm that will handle more than removing/adding between 1 and 2 percentages (≥3)? If so, what is it?

Initial Value = 252
Remove 10% and then a 20% Compound

Based on your answer, I am doing:

252 - (252 * (10/100)) = 226.8
226.8 - (226.8 * (20/100)) = 181.44

However, they are doing:

252 * 0.9 = 226.8
226.8 / 1.2 = 189

Best Answer

First, I will answer your second question. To reduce a number by 10%, you always multiply by 0.9. I don't know the context in which you think you were told that you sometimes divide by 1.1, but I am sure there is something here you have misunderstood. (I have a guess; since you asked about it, I have added it below.)

1: To remove 10% from 200, and then remove a compound 20% from that value:

  1. Remove 10% from 200, giving 200 - 200×10% = 200 - 20 = 180.
  2. Remove 20% from 180, giving 180 - 180×20% = 180 - 36 = 144.

The answer is 144.

2: Your idea here is correct.

3: To add 10% to 200, and then remove a compound 20% from that value:

  1. Add 10% to 200, giving 200 + 200×10% = 200 + 20 = 220.
  2. Subtract 20% from 220, giving 220 - 220×20% = 220 - 44 = 176.

4: You can use your idea from #2 here.

To handle multiple increases or reductions, just do them one step at a time.

I hope this is some help.

Suppose you see a price $p$ and you know that this price was marked up by 10% sometime in the past. You want to know what the original price was before the markup. This is $p ÷ 1.1$.

Notice that this is not the same as if you reduce $p$ by 10%! That would be $p × 0.9$, which is different.

I guess that the reason you thought you might reduce a number by 10% by dividing by 1.1 is that you were confused about this case. It seems as though reducing a number by 10% should be the same as undoing an increase of 10%, but it isn't.

For example, if you see a price of \$110 and you know it was marked up by 10%, then the original price was \$110 ÷ 1.1 = \$100. But to reduce \$110 by 10% you calculate 110 × 0.9 = \$99. Undoing a markup of 10% is not the same as reducing by 10%.

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