# % problem

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A % change for stomach patients within a year from 300 to 360 is:

$\frac{360-300}{300}*100=$ 20%

A % change for liver patients within a year from 200 to 260 is:

$\frac{260-200}{200}*100 =$ 30%

Hence Total % change in stomach and liver patients within a year is:

$\frac {620-500}{500}*100=$ 24%

But it should be 50% shouldn"t it ??

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It looks ok to me - why do you think it should be 50%?

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A 20% change in one population plus a 30% change in another population cannot be added to give a 50% change in a total population

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It looks ok to me - why do you think it should be 50%?

20% change in stomach patients and 30% change in liver patients gives a total 50% and not 24%

A 20% change in one population plus a 30% change in another population cannot be added to give a 50% change in a total population

give me a mathematical or logical reason why not

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Mathematically: Your third equation is a perfect representation of "why not"

Logically: you could create more and more extreme examples. Your system would mean that: An absolute change has a greater and greater effect on the total population as the size of the population which has been changed diminishes - this is clearly logically flawed and can be shown by taking to absurd/extreme lengths. The numbers of people in my office has decreased by 66% today - the number of people in the rest of the world has decreased by .0001% therefore the number of people in the world in total has decreased by 66.0001%.

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20% change in stomach patients and 30% change in liver patients gives a total 50% and not 24%

give me a mathematical or logical reason why not

You can't add the change but not add the total on which that change is based. You have 500 total patients at the start and add 120.

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A % change for stomach patients within a year from 300 to 360 is:

$\frac{360-300}{300}*100=$ 20%

A % change for liver patients within a year from 200 to 260 is:

$\frac{260-200}{200}*100 =$ 30%

Hence Total % change in stomach and liver patients within a year is:

$\frac {620-500}{500}*100=$ 24%

But it should be 50% shouldn"t it ??

No, as imatfaal says you can't just add the percentages.

You need to create a new population with either stomach or a liver complaint, by adding the individual populations of each, just as you have done above.

A small correction to the wording here.

Hence Total % change in stomach and liver patients within a year is:

should be

Hence Total % change in stomach or liver patients within a year is:

Further you have to make the assumption that none of the 300 stomach aptients are also counted in the 200 liver patients.

Otherwise you do not have enough information.

That is no patient has both a stomach and a liver complaint.

Edited by studiot

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give me a mathematical or logical reason why not

Imagine a school classroom of boys and girls.

If 50% of the boys won medals at the annual sports day and 75% of the girls won medals at the annual sports day, do you really think that 125% of the entire class won medals?

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Deleted: on second read I see Studiot beat me to the point I thought I was making.

Edited by pzkpfw

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ok,let's make it easier:

suppose a No goes from 300 to 360,then its %change is:

$\frac{360-300}{300}*100$ =20%

And suppose another No goes from 200 to 260,then its % change is:

$\frac{260-200}{200}*100$ = 30%

Now total % change is :

$\frac{620-500}{500}*100$ = 24%

Since now we have pure Nos and not different populations shouldn't the total % change be 50%

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ok,let's make it easier:

suppose a No goes from 300 to 360,then its %change is:

$\frac{360-300}{300}*100$ =20%

And suppose another No goes from 200 to 260,then its % change is:

$\frac{260-200}{200}*100$ = 30%

Now total % change is :

$\frac{620-500}{500}*100$ = 24%

Since now we have pure Nos and not different populations shouldn't the total % change be 50%

I don't know if that was meant as an answer to my post or not so I will give the benefit of the doubt.

You have been told umpteen times

You can't just add the percentages.

You can certainly simplify something but not to the point where you state it incorrectly.

A number is a number and does not change. You have several different numbers

So 360 is a different number from 300.

300 does not got to 360 that is meaningless.

Let us state your latest post (quoted) correctly.

The difference between two numbers, when expressed as a percentage of the smaller one is given by the equation

$\left( {100} \right)\left( {\frac{{{\rm{Larger - Smaller}}}}{{{\rm{Smaller}}}}} \right)$

You have correctly used this twice to obtain the % difference between 200 and 260 and between 300 and 360 in your first two calculations.

BUT

And I have already said this,

The numbers for the third calculation are different again from any of the first two sets.

As before you have performed this calculation correctly

$\left( {100} \right)\left( {\frac{{{\rm{Difference1 + Difference2}}}}{{{\rm{Smaller1 + Smaller2}}}}} \right)$

Which is equal to

$= \left( {100} \right)\left( {\frac{{{\rm{Larger1 + Larger2 - Smaller1 - Smaller2}}}}{{{\rm{Smaller1 + Smaller2}}}}} \right)$

because you have the

$\left( {100} \right)\left( {\frac{{{\rm{Total}}\;{\rm{Difference}}}}{{{\rm{Total base population}}}}} \right)$

Does this help?

Edited by studiot

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$\frac{Larger_1-Smaller_1}{Smaller_1}*100 +\frac{Lalger_2-Smaller_2}{Smaller_2}*100$

Are you going to get:

$= \left( {100} \right)\left( {\frac{{{\rm{Larger1 + Larger2 - Smaller1 - Smaller2}}}}{{{\rm{Smaller1 + Smaller2}}}}} \right)$ ????

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After several people have made quite an effort to explain an extremely simple problem, the OP has resolutely refused to understand any of it. At this stage there seems no point in trying to explain further. Of course, he/she could be a troll.

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$\frac{Larger_1-Smaller_1}{Smaller_1}*100 +\frac{Lalger_2-Smaller_2}{Smaller_2}*100$

Are you going to get:

$= \left( {100} \right)\left( {\frac{{{\rm{Larger1 + Larger2 - Smaller1 - Smaller2}}}}{{{\rm{Smaller1 + Smaller2}}}}} \right)$ ????

Since you have already demonstrated that you can correctly perform the arithmetic of fractions, I see no reason why you can't work out the answer to this for yourself.

So are they the same?

When you have done that you might like to consider this.

Most people just use the formulae you quoted in your post#1 without thinking about the detail or the rules.

The rules are:

1. The % must all be calculated on the same base.

2. The % must be mutually exclusive. This is why I made such a fuss about the difference between and and or in my post#7

To show this try calulating the following %.

$\left( {100} \right)\left( {\frac{{200}}{{500}}} \right) = a\%$

$\left( {100} \right)\left( {\frac{{260}}{{500}}} \right) = b\%$

$\left( {100} \right)\left( {\frac{{300}}{{500}}} \right) = c\%$

$\left( {100} \right)\left( {\frac{{360}}{{500}}} \right) = d\%$

They are all reckoned on the same base in accordance with rule 1.

now calculate

$\left( {b - a} \right) + \left( {d - c} \right)$

What do you notice?

Edited by studiot

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A % change for stomach patients within a year from 300 to 360 is:

$\frac{360-300}{300}*100=$ 20%

A % change for liver patients within a year from 200 to 260 is:

$\frac{260-200}{200}*100 =$ 30%

Hence Total % change in stomach and liver patients within a year is:

$\frac {620-500}{500}*100=$ 24%

But it should be 50% shouldn"t it ??

To put it extremely simply, you are mixing 2 pools of people into one. 20% of stomach patients are from a different pool than the 30% of liver patients.

If person A has 10 apples and person B has 10 bananas, and they are each given an additional 5 of their fruit respectively, you would say there is was an 100% increase in fruit, whereas there was only a 50% increase in their fruit.

This is because the added change was 10 out of 20 fruit, and not 10/10.

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Since you have already demonstrated that you can correctly perform the arithmetic of fractions, I see no reason why you can't work out the answer to this for yourself.

So are they the same?

When you have done that you might like to consider this.

Most people just use the formulae you quoted in your post#1 without thinking about the detail or the rules.

The rules are:

1. The % must all be calculated on the same base.

2. The % must be mutually exclusive. This is why I made such a fuss about the difference between and and or in my post#7

To show this try calulating the following %.

$\left( {100} \right)\left( {\frac{{200}}{{500}}} \right) = a\%$

$\left( {100} \right)\left( {\frac{{260}}{{500}}} \right) = b\%$

$\left( {100} \right)\left( {\frac{{300}}{{500}}} \right) = c\%$

$\left( {100} \right)\left( {\frac{{360}}{{500}}} \right) = d\%$

They are all reckoned on the same base in accordance with rule 1.

now calculate

$\left( {b - a} \right) + \left( {d - c} \right)$

What do you notice?

Nothing

To put it extremely simply, you are mixing 2 pools of people into one. 20% of stomach patients are from a different pool than the 30% of liver patients.

If person A has 10 apples and person B has 10 bananas, and they are each given an additional 5 of their fruit respectively, you would say there is was an 100% increase in fruit, whereas there was only a 50% increase in their fruit.

This is because the added change was 10 out of 20 fruit, and not 10/10.

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I did read it and you're repeating the same thing over again. You seem to be confused about it so I tried to give the simplest and most elaborate explanation of why you cannot add percentages like that. I was quite satisfied with the example and I thought you would acknowledge it for sure.

Studiot put some more effort into the explanation and went into more detail. You should be thankful, instead of being so dissmisive that you ignored his post. There are people who actually know mathematics well on this forum and you should at least put some effort into understanding what they wrote.

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You can think of it this way, which was also covered by others:

# of people you add to those 500 = 120

What % of 500 people do 120 people make?

(120/500)*100 = 24%

To get 50%, you would need to add 250 people instead of 120. If it's not obvious to you just looking at it, then work it backwards:

50 = (x/500)*100 ; where x is # of people you need to add in order to get 50%

x = (50/100)*500 = 250

(Sorry I could not figure out how to write Math equations using text editor -- mod can feel free to edit my post so it looks nicer and is easier to read)

Edited by Sicarii

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Mathematics certainly is not the science that you can make stories out of nothing

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