The difference between a two-digit number and the number obtained by interchanging the digits is $36$. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is $1:2$?

Let the two-digit number be $10x+y$, where $x$ is the tens digit and $y$ is the units digit.
The number obtained by interchanging the digits is $10y+x$.

According to the question, the difference between the numbers is $36$:

$$|(10x+y)-(10y+x)|=36$$

$$9|x-y|=36⟹|x-y|=4$$

We are given that the ratio between the digits of the number is $1:2$.
Let the digits be $k$ and $2k$.
The absolute difference between the digits is:

$$|2k-k|=k$$

Since we found $|x-y|=4$, we have:

$$k=4$$

Thus, the digits are $4$ and $8$.

* The sum of the digits is: $S=8+4=12$
* The difference of the digits is: $D=8-4=4$

The question asks for the difference between the sum and the difference of the digits:

$$\text{Required Value}=S-D=12-4=8$$