The selling price of 8 articles is same as the cost price of 10 articles. What is profit %?

Options

A. `25%`
B. `20%`
C. `22%`
D. `33%`

Answer

To solve the problem, we need to determine the profit percentage based on the information given about the selling price and cost price of articles.

### Step-by-Step Solution:

1. **Understand the Relationship**:
- The selling price (SP) of 8 articles is equal to the cost price (CP) of 10 articles.
- This can be expressed as:
\[ SP(8) = CP(10) \]

2. **Let’s Define Variables**:
- Let the cost price of one article be \( CP \).
- Therefore, the cost price of 10 articles is:
\[ CP(10) = 10 \times CP \]
- Let the selling price of one article be \( SP \).
- Therefore, the selling price of 8 articles is:
\[ SP(8) = 8 \times SP \]

3. **Set Up the Equation**:
- From the relationship established, we can write:
\[ 8 \times SP = 10 \times CP \]

4. **Express Selling Price in Terms of Cost Price**:
- Rearranging the equation gives us:
\[ SP = \frac{10 \times CP}{8} = \frac{5 \times CP}{4} \]

5. **Calculate Profit**:
- Profit is defined as:
\[ Profit = SP - CP \]
- Substitute \( SP \) from the previous step:
\[ Profit = \frac{5 \times CP}{4} - CP \]
- To combine the terms, express \( CP \) as \( \frac{4 \times CP}{4} \):
\[ Profit = \frac{5 \times CP}{4} - \frac{4 \times CP}{4} = \frac{1 \times CP}{4} \]

6. **Calculate Profit Percentage**:
- Profit percentage is given by:
\[ Profit \% = \left( \frac{Profit}{CP} \right) \times 100 \]
- Substitute the profit:
\[ Profit \% = \left( \frac{\frac{1 \times CP}{4}}{CP} \right) \times 100 = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer:
The profit percentage is **25%**.