Misunderstanding of percentage increase If something increase $50$ to $200$, I know that it is $400\%$ increment using common sense.
I can get this using $\dfrac{200}{50}\times 100\% =  400\%$.
If something increase $50$ to $52$, I know that it is $4\%$ increment using common sense.
But if I apply the same logic, $\dfrac{52}{50}\times 100\% = 104\%$.
What is the problem in my logic? 
 A: If something increases from $50$ to $200$, it increases by $300\%$ and has a new value that is $400\%$ of the old value. 
Similarly, if something increases from $50$ to $52$, it increases by $4\%$ to a new value that is $104\%$ of the old one.
A: Percentage increase is $$\frac{\text{new number - old number}}{\text{old number}}\times 100 \%$$
The right comptuation should be $$\frac{200-50}{50} \times 100 \%=300\%$$
A: You are making the classic mistake of confusing ratio with change.
$ratio = \frac{new\;value}{old\;value}$
$percentage\;ratio = \frac{new\;value}{old\;value} \times  100\%$
$difference = new\;value - old\;value$
$percentage\;change = \frac{difference}{old\;value} \times  100\% = \frac{new\;value - old\;value}{old\;value} \times  100\%$
Change is more commonly known as growth or increase.
A: This is were the ratio makes more sense 
That is when 
50:400 
are divided one both sides by 50 giving us
1:8 
so my understanding is that it is eight times more.
A: The convention is that "percentage increase" is the number of percentage points that are added.
So it is assumed that you always start with $100\%$ of a number and then add an $n\%$ percent increase to that, so you end up with $(100 + n)\%$ of the original number.
If you take the ratio of the starting and ending amounts and multiply by $100\%,$
you end up with the figure $(100 + n)\%.$ You then have to subtract $100\%$ if what you want is the percentage increase.
Indeed $52$ is $104\%$ of $50,$  but the added amount is only $2,$ which is $4\%$ of $50.$
Likewise $200$ is $400\%$ of $50,$ but the added amount is only $150,$ which is $300\%$ of $50.$
A: If you see your question, you'll see that you have answered it yourself. In the second statement, you said 50 to 52 increment means 4% which is equal to 100 subtracted from 104 which you have calculated. Similarly, if you subtract 100 from 400 you will get 300%.
