Misunderstanding of percentage increase

Question

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?

Answer 1

Percentage increase is $$\frac{\text{new number - old number}}{\text{old number}}\times 100 \%$$

The right comptuation should be $$\frac{200-50}{50} \times 100 \%=300\%$$

Answer 2

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.

Answer 3

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 $50.$

Answer 4

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.

Answer 5

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 $300$%.

Answer 6

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.