The hundred digit of a three digit number is 7 more than the unit digit. The digits of the number are reversed and the resulting number is subtracted from the original three digit number. The unit digit of the final number, so obtained is

Options

A. 0
B. 1
C. 2
D. 3

Answer

To solve the problem step-by-step, let's break it down clearly:

### Step 1: Define the digits of the three-digit number
Let the three-digit number be represented as \( ABC \), where:
- \( A \) is the hundreds digit,
- \( B \) is the tens digit,
- \( C \) is the units digit.

### Step 2: Establish the relationship between the digits
According to the problem, the hundreds digit \( A \) is 7 more than the units digit \( C \). This can be expressed mathematically as:
\[ A = C + 7 \quad \text{(1)} \]

### Step 3: Write the original and reversed numbers
The original three-digit number can be expressed as:
\[ 100A + 10B + C \quad \text{(2)} \]
The reversed number, which is \( CBA \), can be expressed as:
\[ 100C + 10B + A \quad \text{(3)} \]

### Step 4: Set up the subtraction
Now, we need to subtract the reversed number from the original number:
\[ (100A + 10B + C) - (100C + 10B + A) \]

### Step 5: Simplify the subtraction
Now, let's simplify the expression:
\[ (100A + 10B + C) - (100C + 10B + A) = 100A + 10B + C - 100C - 10B - A \]
The \( 10B \) terms cancel out:
\[ = 100A - A + C - 100C = 99A - 99C \]
Factoring out the common term:
\[ = 99(A - C) \quad \text{(4)} \]

### Step 6: Substitute the relationship from Step 2
From equation (1), we know that \( A - C = 7 \). Substituting this into equation (4):
\[ = 99 \times 7 = 693 \]

### Step 7: Determine the unit digit of the result
The result of the subtraction is 693. The unit digit of 693 is:
\[ \text{Unit digit} = 3 \]

### Conclusion
Thus, the unit digit of the final number obtained after the subtraction is:
\[ \boxed{3} \]