If 50% of a number is added to 75, then the result is the number itself.The number is `:`

Options

A. a) 150
B. b) 400
C. c) 100
D. d) 250

Answer

To solve the problem step by step, let's denote the unknown number as \( X \).

### Step 1: Understand the problem
The problem states that if 50% of a number is added to 75, the result equals the number itself.

### Step 2: Set up the equation
We can express 50% of the number \( X \) as \( \frac{50}{100} \times X = \frac{X}{2} \). According to the problem, we can write the equation:
\[ \frac{X}{2} + 75 = X \]

### Step 3: Rearrange the equation
To isolate \( X \), we can rearrange the equation:
\[ \frac{X}{2} + 75 = X \]
Subtract \( \frac{X}{2} \) from both sides:
\[ 75 = X - \frac{X}{2} \]
This simplifies to:
\[ 75 = \frac{X}{2} \]

### Step 4: Solve for \( X \)
To find \( X \), we can multiply both sides of the equation by 2:
\[ X = 75 \times 2 \]
\[ X = 150 \]

### Conclusion
The number is \( 150 \).