The difference between a two-digit number and the number obtained by interchanging the position of its digits is 36. What is the difference between the two digits of that number?

Options

A. 3
B. 4
C. 9
D. Cannot be determined

Answer

To solve the problem, we will define the two-digit number and set up an equation based on the information given.

### Step-by-Step Solution:

1. **Define the Digits**:
Let the two-digit number be represented as \( 10y + x \), where \( y \) is the digit in the tens place and \( x \) is the digit in the units place.

2. **Interchange the Digits**:
When the digits are interchanged, the new number becomes \( 10x + y \).

3. **Set Up the Equation**:
According to the problem, the difference between the original number and the number obtained by interchanging the digits is 36. Therefore, we can write the equation:
\[ (10y + x) - (10x + y) = 36 \]

4. **Simplify the Equation**:
Simplifying the left side of the equation:
\[ 10y + x - 10x - y = 36 \]
This simplifies to:
\[ 9y - 9x = 36 \]

5. **Factor Out Common Terms**:
We can factor out 9 from the left side:
\[ 9(y - x) = 36 \]

6. **Solve for the Difference**:
Dividing both sides by 9 gives:
\[ y - x = 4 \]

### Conclusion:
The difference between the two digits of the number is \( 4 \).