The position of the digit of a two digit number are interchanged. If the sum of the original number and the number obtained by interchanging the digit is 44. What is the sum of digit of that number ?

Options

A. 2
B. 4
C. 11
D. Cannot be determined

Answer

To solve the problem, let's denote the two-digit number as \( 10a + b \), where \( a \) is the digit in the tens place and \( b \) is the digit in the units place.

### Step 1: Set up the equation
When the digits are interchanged, the new number becomes \( 10b + a \). According to the problem, the sum of the original number and the number obtained by interchanging the digits is 44. Therefore, we can write the equation:

\[ (10a + b) + (10b + a) = 44 \]

### Step 2: Simplify the equation
Now, let's simplify the equation:

\[ 10a + b + 10b + a = 44 \]

Combining like terms gives us:

\[ 11a + 11b = 44 \]

### Step 3: Factor out common terms
We can factor out 11 from the left side:

\[ 11(a + b) = 44 \]

### Step 4: Solve for the sum of the digits
Now, divide both sides by 11:

\[ a + b = \frac{44}{11} \]

This simplifies to:

\[ a + b = 4 \]

### Conclusion
The sum of the digits of the two-digit number is \( 4 \).

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