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I'd like to check if a formula I have been using is wrong.

I am studying and came across the following in how to calculate the percent increase/decrease of a value:

% increase = Increase ÷ Original Number × 100

For example if I buy a product for 2 and sell it for 4, the formula is:

(4-2)/2 x100 = 100% increase.

I get all of this. My issue is that I was using another formula until I came across this one (which is obviously wrong in this context) and I am amazed I have had it wrong for so many years; I feel as if it is a valid formula which I was taught a long time ago and maybe I am just applying it wrong, it is:

new value /orginal value x100

So in this example we would have:

4/2x100 = 200%

My question is, in what context do you use this forumla (if at all)?

Sorry for the somewhat vague question, it's just I can't remember how I aquired this formula; my memory is usually very good, which is why I feel as if it is used in some context and I have just mixed it up with something else.

Thanks,

Mucker
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  • The second formula is the relative amount, expressed as a percentage. For example, if you want to know whether someone makes less than $80%$ of the median income in their geographic area, you could take their income, divide by the median income, multiply by $100%,$ and compare to $80%.$ – David K Nov 03 '21 at 02:13
  • Thanks. I seem to recall it being used when someone talks about a percent of profit you made ie (for same example above) they would say "you made a 200% profit" or "it increased by a factor of 200%". Would either of those statement be correct? – Mucker Nov 03 '21 at 02:17
  • "Increased by a factor of $200%$" is correct for your example, although it can be tricky to use -- suppose the next time you buy at price $2$ and sell at price $1,$ is that an "increase by a factor of $50%$"? I think it's a decrease, but decrease by a factor can be ambiguous. Buying at $4$ and selling at $2$ I would say you got $100%$ profit, not $200%$; suppose next time you buy at $2$ and sell at $2$, there is no profit, so $0%$ profit is an accurate way to describe it. – David K Nov 03 '21 at 02:23
  • @DavidK that is where I was going with this and what prompted the question. I was confused by the ambiguity you mention. Good to see I was right after all - the question came from writing an answer saying "it increased by a factor of 200%" but then I read about profit increase which came out at 100% increase. I guess I am best avoiding "by a factor of..."? – Mucker Nov 03 '21 at 03:30
  • so to summarise and confirm I understand it now - "increasing by a factor of x%" is not the same as saying "increase by a profit of x%"? They are so very similar and I guess I thought they meant the same hence my confusion – Mucker Nov 03 '21 at 03:32

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