Using the percentage difference formula, explained here, with the numbers $1$ and $1.5$, I have a result of $40\%$.
So, if i have a $100$ value, how can I find two numbers with a formula that add up to $100$ with the same $40\%$ percentage difference? For example, $60$ and $40$ have a difference of $40\%$ and $60 + 40 = 100$
i.g., for $4$ and $16$: $\frac{|4-16|}{(4+16)/2} * 100 = 120\% $, I would need two values that $x + y = 100$ and $\frac{|x-y|}{(x+y)/2} * 100 = 120\% $
Here is a useful and simple calculator for percentage difference.
This is my first question and I'm not very good at math or English, so I'm sorry for any mistakes.
Best Answer
To solve your question in a general manner, first note there's the required condition
$$x + y = 100 \tag{1}\label{eq1A}$$
Since your equations are symmetric in $x$ and $y$, then WLOG have $x \ge y \implies \lvert x - y \rvert = x - y$. Next, using $120\% = \frac{120}{100} = 1.2$ gives that
$$\begin{equation}\begin{aligned} \frac{x - y}{(x + y)/2} & = 1.2 \\ \frac{x - y}{100/2} & = 1.2 \\ x - y & = 1.2(50) \\ x - y & = 60 \end{aligned}\end{equation}\tag{2}\label{eq2A}$$
Now, adding \eqref{eq1A} and \eqref{eq2A} results in
$$2x = 160 \implies x = 80 \tag{3}\label{eq3A}$$
Using this in \eqref{eq1A} then gives
$$80 + y = 100 \implies y = 20 \tag{4}\label{eq4A}$$
Since you already have that $4$ and $16$ give the required difference percentage, here is a bit shorter and easier way to solve the problem. Note that for any $c \neq 0$, we get
$$\begin{equation}\begin{aligned} \frac{\lvert cx - cy \rvert}{(cx + cy)/2} & = \frac{c\lvert x - y \rvert}{c(x + y)/2} \\ & = \frac{\lvert x - y \rvert}{(x + y)/2} \end{aligned}\end{equation}\tag{5}\label{eq5A}$$
i.e., multiplying both $x$ and $y$ by $c$ (and, thus, the sum of them) results in the same value difference percentage. Thus, since $4 + 16 = 20$ and $\frac{100}{20} = 5$, we can use $c = 5$ to directly get that the values of $x$ and $y$ are $4 \times 5 = 20$ and $16 \times 5 = 80$.