Sorry but stuck on stupid on this one.
If I have a random number – let’s say 545 and I reduce it by 20%. It’s reduced by 109 making it 436.
But if I want to increase it back to 545 I have to add 25%
Edit: Ahhhh Thank you all for this! Makes perfect sense now!
In: Mathematics
Yes. Obviously, the 20% of a larger number is not the same as 20% of a smaller number, so you gotta adjust it if you want to get back where you started.
reduced by 20% means multiply by 0.8
increase by 20% means multiply by 1.2
0.8 * 1.2 does not equal 1, so reduce by 20% then increase by 20% does not get you back to the original number
but 0.8 * 1.25 (so i crease by 25%) is equal to 1, so you do get the original back
It may sound obvious, but the answer is “545 and 436 are different numbers”.
20% of 545 is 109, but 20% of 436 is 87.
In math the reciprocal of a number is 1 divided by the number. the number times it’s reciprocal is equal to 1. when you reduce a number by 20% you are multiplying it by (1-0.20) or 0.80
Therefore 545*0.80*(1/0.80) = 545. (1/0.80) = 1.25.
this is also to say 4/5 = 0.80 and 5/4 = 1.25.
If you multiply something by 4/5 (80%), you have to multiply it by 5/4 (125%) to get the original value back.
We can use different and easier numbers to visualize it.
If we have 100 something and decrease it by 50%, it’s the same as
100 * 0,5 = 50
100 – 50 = 50
100 / 2 = 50
But if we take the 50 something and increase it by 50%, it’s the same as
50 * 1,5 = 75
50 + 25 = 75
50 / 0,6666… = 75
Different starting points have different weights in percentage
It struck me when you think about what you’re actually doing when you do percentages, which is multiplying by a decimal and that the opposite of multiplication is division.
So…
545 * 0.8 = 436
436 / 0.8 = 545
and dividing something by 0.8 = multiplying by 1.25 which is what causes the confusion.
1 / 0.8 = 1.25
This reminds me of when I first got into sales and was confused by gross profit margin. I learned a neat little trick that works with many of these situations including the one you just mentioned. If you reduce by 20% (1/5) then you need to increase the result by 25% (1/4) to get back to the same number. By the same token reducing by 1/3 you’d need to increase by one half. The Delta is always the denominator plus or minus one.
Btw, to clarify how gross profit margin comes into this, if you want 20% gross profit margin then you need to increase your sales price 25% over your cost.
all correct answers but to make it even simpler than some of these, to get back to your original value you just do the opposite operation
545 reduced by 20% could be written as 545*0.8 = 436
you do the opposite operation….436/0.8 = 545
or
545 – (545*.2) = 436, which the opposite is 436 + (545*0.2), where you are “adding back” 20% of the original value (which is what you took away in the first place)
dividing by 4/5 is the same as multiplying by 5/4
I started with 545. I reduce it by 20% of 545 to 434.
To get back to the original number, I need to increase it again by 20% of 545. But clearly 20% of 545 is more than 20% of 436, so I need to add more than 20% (namely 25%) of 436.
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