if 100 x 1.17 (17%) = 117, how can I know how many % I have to deduct 117 to get 100? Obviously, this is no more 17%.
The same can be applied if 100 - 10% = 90. Then how many % I have to add to 90 to get 100? Again, it is no more 10%.
I know how to calculate this, but I was wondering if there is a math formula for this? something as simple as a*b=c => b=c/a
Just use percentage of increase/decrease.
$$\frac{b-a}{a}$$
Where $a$ is the initial value and $b$ is the final value.
$$\frac{100-117}{117} = -\frac{17}{117} \approx -0.14523$$
Multiplying the value by $100$% gives the percentage. So, subtracting $14.523$% of $117$ from $117$ will give $100$.
Just remember that when $b > a$, the answer will be positive, so there is a percentage increase (must be added), but when $b < a$, the answer will be negative, so there is a percentage increase (which must be subtracted).
Increasing something by $r\%$ means multiplying it by $1+r$ - a fact you seem to know.
In fact changing by $r\%$ means multiplying it by $1+r$ even when $r$ is negative, so a decrease. To see that, think of "$25\%$ off" as "multiply by $1-0.25 = 0.75$".
So the simple formula you want to undo an increase of $r\%$ is to multiply by $1/1+r$. If you really need to separate out the actual percent change, it's just $$ \frac{1}{1+r} -1 = -\frac{r}{1+r}. $$
To check that, note that it tells you that to undo a $100\%$ increase, which corresponds to $r=1$, you need a $50\%$ decrease.
