Problem:
Find a two-digit number if it is 36 less than the number obtained by interchanging the digits. The sum of the digits is 12.

Solution:
Let's assume that the two-digit number is represented as "10x + y," where x and y are the two digits of the number. To find the number, we need to follow the given conditions.

Condition 1: The number is 36 less than the number obtained by interchanging the digits.
The number obtained by interchanging the digits is represented as "10y + x." According to the first condition, we have:
10x + y = (10y + x) - 36

Condition 2: The sum of the digits is 12.
The sum of the digits x and y should be equal to 12. So, we have another equation:
x + y = 12

Now, let's solve these equations simultaneously to find the values of x and y.

Solving the Equations:
From the second equation, we have:
x = 12 - y

Substituting this value of x into the first equation, we get:
10(12 - y) + y = (10y + (12 - y)) - 36
120 - 10y + y = 10y + 12 - y - 36
120 - 9y = 9y - 24

Simplifying further:
120 + 24 = 9y + 9y
144 = 18y
y = 8

Substituting this value of y into the second equation, we get:
x + 8 = 12
x = 12 - 8
x = 4

Therefore, the two-digit number is 48.

Answer:
The two-digit number is 48, which is 36 less than the number obtained by interchanging the digits. The sum of the digits 4 and 8 is indeed 12.