adding %: We define a % increase of a No from a value x to another value y, y>x,...

[chrislav]

adding %: We define a % increase of a No from a value x to another value y, y>x,...

We define a % increase of a No from a value x to another value y, y>x ,as :

\(\displaystyle \frac{y-x}{x}*100\)

Suppose now 300 goes to 360 .Then we have a % increase of :

\(\displaystyle \frac{360-300}{300}*100\)= 20%

And suppose 400 goes to 600. Then we have a % increase of :

\(\displaystyle \frac{600-400}{400}*100\) = 50%

Now total % increase of both Nos is:

\(\displaystyle \frac{(360+600)-(300+400)}{700}*100\)= 37,1%

But it should be 20% +50% = 70% shouldn't it

 

[Deleted member 4993]

We define a % increase of a No from a value x to another value y, y>x ,as :

\(\displaystyle \frac{y-x}{x}*100\)

Suppose now 300 goes to 360 .Then we have a % increase of :

\(\displaystyle \frac{360-300}{300}*100\)= 20%

And suppose 400 goes to 600. Then we have a % increase of :

\(\displaystyle \frac{600-400}{400}*100\) = 50%

Now total % increase of both Nos is:

\(\displaystyle \frac{(360+600)-(300+400)}{700}*100\)= 8,57 % ← Incorrect

But it should be 20% +50% = 70% shouldn't it ............ No...

\(\displaystyle \frac{(360+600)-(300+400)}{700}*100 \ = \frac{260}{7}\)% \(\displaystyle \ = \ 37. 1\)%

 

[chrislav]

\(\displaystyle \frac{(360+600)-(300+400)}{700}*100 \ = \frac{260}{7} \ = \ 37. 1\)%

Thanks ,you are right it is 37,1%

But why the indivitual %,s shouldn't add up to 37,1%

 

[mmm4444bot]

But why the individual %s shouldn't add up to 37,1?

Percent change does not progress that way because, each time you complete a change, the size of a unit percentage is not the same as it previously was. (Also, you skipped the percent change from 360 to 400.)

For example, if we start with 1, and we increase it by 1% one-hundred times in a row, we will not have increased 1 by a total of 100%. Instead of 2, we'll get 2.7048 (rounded).

1% of 1 is 0.01 (the first change increases 1 to 1.01).

1% of 1.01 is 0.0101, slightly larger than the previous 1% (the second change increases 1.01 to 1.0201).

That was two 1% increases, yet the percent change from 1 to 1.0201 is 2.01%, not 2%. :cool: