If cost price of 80 article is equal to the selling price of 50 articles, then what will be the profit percentage?

Options

A. `25%`
B. `40%`
C. `60%`
D. `37.5%`

Answer

To solve the problem, we need to find the profit percentage given that the cost price of 80 articles is equal to the selling price of 50 articles.

### Step-by-Step Solution:

1. **Define Variables**:
Let the cost price (CP) of one article be \( x \) and the selling price (SP) of one article be \( y \).

2. **Set Up the Equation**:
According to the problem, the cost price of 80 articles is equal to the selling price of 50 articles. This can be expressed mathematically as:
\[ 80x = 50y \]

3. **Rearrange the Equation**:
To find the ratio of selling price to cost price, we can rearrange the equation:
\[ \frac{y}{x} = \frac{80}{50} \]
Simplifying the right side:
\[ \frac{y}{x} = \frac{8}{5} \]

4. **Express Selling Price in Terms of Cost Price**:
From the ratio, we can express the selling price in terms of cost price:
\[ y = \frac{8}{5}x \]

5. **Calculate Profit**:
Profit is defined as:
\[ \text{Profit} = \text{SP} - \text{CP} = y - x \]
Substituting \( y \):
\[ \text{Profit} = \frac{8}{5}x - x = \frac{8}{5}x - \frac{5}{5}x = \frac{3}{5}x \]

6. **Calculate Profit Percentage**:
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{\frac{3}{5}x}{x}\right) \times 100 = \left(\frac{3}{5}\right) \times 100 \]
Simplifying:
\[ \text{Profit Percentage} = 60\% \]

### Final Answer:
The profit percentage is **60%**.