# How to reverse percentage?

If I have a value of 25%, and I want the value as it would be on the opposite side of the halfway point (75% in this case), what is a formula that can calculate this?

I don't know the appropriate tags for this so feel free to adjust them. However, it is a programming-related question.

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You answered your own question or I didn't understand what you mean. Could you be more explicit? –  Raskolnikov Nov 17 '10 at 20:49
Yes, how to find the second value based on the first. so if it wasn't 25%, instead it was 31.04%, how to find the opposite across the halfway point. –  just_another_coder Nov 17 '10 at 20:51

It's unclear to me what it is you want. One possible interpretation is that you know how much 25\% is, and you want to know how much 75\% is. For this situation it is very easy: if $c$ is 25% of some unknown quantity $y$, and you want to know how much 75% of $y$ is, it is $3c$. For instance, if you know that $27$ is 25% of something, then $3(27)=81$ is 75% of that same something.

The Rule of Three will let you figure out how much $q$% is if you know what $p$% is. If you know that $c$ is $p$% of an unknown quantity, and you want to know how much $q$% of that same quantity will be, then you can set it up as a cross-multiplication problem: $$\begin{array}{ccc} c & \text{---} & p\\ x & \text{---} & q \end{array}$$ so that $x=qc/p$. For example, if you know that $23$ is $17$% of some unknown quantity $x$, and you would like to know who much 77% of that same quantity would be, it is $23(77/17) \approx 104.176$.

But after writing all of the above it strikes me that the question may be even more basic: you have a certain quantity $p$ between $0$ and $50$, which you interpret as a percentage, and you want to know what quantity $q$ is just as far from $50$ but "on the other side". Since you want $q-50 = 50-p$, then you want $q=100-p$.

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Apologies for my poor explanation. If I know the percentage of one object, I want to get the reverse of it. So if a wall was 100 meters high, and 25m up was 25%, how to find the opposite. I don't know how to express 'opposite' properly in mathematical terms. In this case it would be 75%. If the initial value was 34.04, then the answer would be 65.96 percent. I've posted a working solution below. –  just_another_coder Nov 17 '10 at 21:11
@just_another_coder: you are still not doing very well in explaining what you mean. Do you mean merely, what percentage q is as far above 50% as 50% is from 34.04%? Then see my last line. –  Arturo Magidin Nov 17 '10 at 21:14
Thanks. Yes, it's very basic. But my math is horrible. –  just_another_coder Nov 17 '10 at 21:16

Unless I completely missed the point of the question, the answer is rather trivially $100\% - p$.

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Never mind, it's:

(100 - 25) or (100 - 34.04)

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I don't see the number 34.04 anywhere in the original question. Where did it come from? –  Ross Millikan Nov 17 '10 at 21:01
From a comment above. –  just_another_coder Nov 17 '10 at 21:08

Given X and Z, you know that X = Y + Z%(Y).

He wants to get Z%(Y)/X.

For example, if Z%=1/5, then I can say that Z%(Y) = (1/6)X. Using percents, Z is 20 (20%=1/5), and Z%(Y) ~ 16.67(X).

This is great if your Z% evaluates to a 1/N fraction, but not so good if your Z% is, say, 9.5%.

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Simply put, to solve for x (in your example, X is the value of 75% of Y)

x = (100*y)/(100*z)

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