Final answer:
The difference between the sum and the difference of the digits of a number with a ratio of 1:2 among its digits, and for which the difference between the number and the number with the digits interchanged is 36, is 8.
Step-by-step explanation:
Let the two digits of the number be x and y with x being the tens digit and y being the units digit.
Given that the ratio of the digits is 1:2, we can say y = 2x.
The value of the two-digit number can be expressed as 10x + y and the value of the number with the digits interchanged is 10y + x.
The difference between the two numbers is 36, so the equation is 10y + x - (10x + y) = 36.
Substituting y with 2x yields 20x + x - 10x - 2x = 36, which simplifies to 9x = 36.
Solving for x gives x = 4, and since y = 2x, y = 8.
The difference between the digits y - x is 8 - 4 = 4, and the sum of the digits y + x is 8 + 4 = 12.
The difference between the sum and the difference of the digits is 12 - 4 = 8,
therefore, the correct answer is (b) 8.