In the cost price of 20 articles is equal to the selling price of 15 articles then find the profit or loss percentage.

Options

A. `20% `loss
B. 25% profit
C. `33.(1)/(3)%` profit
D. 25% loss

Explanation

To solve the problem, we need to find the profit or loss percentage when the cost price of 20 articles is equal to the selling price of 15 articles.

### Step-by-step Solution:

1. **Identify Variables**:
- Let the cost price (CP) of 1 article be \( CP \).
- Therefore, the cost price of 20 articles is \( 20 \times CP \).
- Let the selling price (SP) of 1 article be \( SP \).
- Therefore, the selling price of 15 articles is \( 15 \times SP \).

2. **Set Up the Equation**:
- According to the problem, the cost price of 20 articles is equal to the selling price of 15 articles:
\[ 20 \times CP = 15 \times SP \]

3. **Express Selling Price in Terms of Cost Price**:
- Rearranging the equation gives:
\[ SP = \frac{20 \times CP}{15} \]
- Simplifying this:
\[ SP = \frac{4}{3} \times CP \]

4. **Calculate Profit**:
- Profit is defined as:
\[ \text{Profit} = SP - CP \]
- Substituting the value of SP:
\[ \text{Profit} = \frac{4}{3} \times CP - CP \]
- To combine the terms, convert \( CP \) to a fraction:
\[ \text{Profit} = \frac{4}{3} \times CP - \frac{3}{3} \times CP = \frac{1}{3} \times CP \]

5. **Calculate Profit Percentage**:
- Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
- Substituting the profit we calculated:
\[ \text{Profit Percentage} = \left( \frac{\frac{1}{3} \times CP}{CP} \right) \times 100 = \frac{1}{3} \times 100 \]
- Simplifying this gives:
\[ \text{Profit Percentage} = \frac{100}{3} \approx 33.33\% \]

6. **Final Answer**:
- The profit percentage is \( 33 \frac{1}{3}\% \).