If the sum of digits is 9and the diference between the digit in the ten's place and unit's place is 1, then the two -- digit number is ?
A. 45
B. 63
C. 54
D. 72

Options

A. C
B. A
C. B
D. D

Answer

To solve the problem, we need to find a two-digit number that meets the following criteria:

1. The sum of the digits is 9.
2. The difference between the digit in the ten's place and the unit's place is 1.

Let's denote the two-digit number as \( AB \), where \( A \) is the digit in the ten's place and \( B \) is the digit in the unit's place.

### Step 1: Set up the equations based on the conditions.
From the problem, we can derive the following equations:
1. \( A + B = 9 \) (the sum of the digits)
2. \( A - B = 1 \) (the difference between the ten's place and unit's place)

### Step 2: Solve the equations.
We can solve these equations simultaneously.

From equation (2), we can express \( A \) in terms of \( B \):
\[ A = B + 1 \]

Now, substitute this expression for \( A \) into equation (1):
\[ (B + 1) + B = 9 \]

Combine like terms:
\[ 2B + 1 = 9 \]

Subtract 1 from both sides:
\[ 2B = 8 \]

Now, divide by 2:
\[ B = 4 \]

### Step 3: Find \( A \).
Now that we have \( B \), we can find \( A \) using the expression we derived earlier:
\[ A = B + 1 = 4 + 1 = 5 \]

### Step 4: Form the two-digit number.
Now we have both digits:
- \( A = 5 \)
- \( B = 4 \)

Thus, the two-digit number is \( 54 \).

### Conclusion:
The two-digit number that satisfies both conditions is **54**.