When half of a number is increased by 16, the result is 40. The sum of digits of the original number is

Options

A. 6
B. 7
C. 9
D. 12

Answer

To solve the problem step by step, we will first define the unknown number and then set up an equation based on the information given in the question.

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Set up the equation
According to the problem, when half of the number is increased by 16, the result is 40. We can express this mathematically as:
\[ \frac{x}{2} + 16 = 40 \]

### Step 3: Isolate the term with \( x \)
To isolate \( \frac{x}{2} \), we subtract 16 from both sides of the equation:
\[ \frac{x}{2} = 40 - 16 \]
\[ \frac{x}{2} = 24 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \) by multiplying both sides of the equation by 2:
\[ x = 24 \times 2 \]
\[ x = 48 \]

### Step 5: Find the sum of the digits of the original number
Now that we have found \( x \), which is 48, we need to find the sum of its digits:
\[ 4 + 8 = 12 \]

### Final Answer
The sum of the digits of the original number is \( 12 \).

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