If an article is sold at `1/2` of the total selling price, the loss is 12.5%. Find his profit percentage.

Options

A. 0.75
B. 0.65
C. 0.5
D. 0.6

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript while ensuring clarity in each step.

### Step-by-Step Solution:

1. **Understanding the Selling Price**:
Let the total selling price be \( SP \). According to the problem, the article is sold at half of the total selling price. Therefore, we can express this as:
\[ \text{Selling Price (SP)} = \frac{1}{2} SP = \frac{1}{2} x \]
where \( x \) is the total selling price.

2. **Loss Calculation**:
We know that there is a loss of 12.5%. This can be expressed in fraction form as:
\[ \text{Loss} = \frac{12.5}{100} = \frac{1}{8} \]
If the cost price (CP) is represented as \( CP \), then the selling price after a loss can be calculated as:
\[ SP = CP - \text{Loss} \]
Thus, we can express the selling price in terms of cost price:
\[ SP = CP - \frac{1}{8} CP = \frac{7}{8} CP \]

3. **Setting Up the Equation**:
From our earlier expressions, we have:
\[ \frac{1}{2} x = \frac{7}{8} CP \]
To find \( CP \), we can rearrange this equation:
\[ CP = \frac{8}{7} \cdot \frac{1}{2} x = \frac{4}{7} x \]

4. **Finding the Total Selling Price**:
We also know that the total selling price \( x \) can be expressed in terms of \( CP \):
\[ SP = x \]
Therefore, we can substitute \( CP \) back into our equation:
\[ x = \frac{7}{8} CP \]
By substituting \( CP = \frac{4}{7} x \) into this equation, we can find \( x \).

5. **Calculating the Profit**:
Now, we can calculate the profit:
\[ \text{Profit} = SP - CP = x - \frac{4}{7} x = \frac{3}{7} x \]

6. **Profit Percentage**:
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{3}{7} x}{\frac{4}{7} x} \right) \times 100 = \left( \frac{3}{4} \right) \times 100 = 75\% \]

### Final Answer:
The profit percentage is **75%**.