If selling price of 39 articles is equal to the cost price of 42 articles, then what will be the profit percentage?

Options

A. `8.33`
B. `7.69`
C. `9.09`
D. `11.33`

Answer

To solve the problem, we need to find the profit percentage given that the selling price of 39 articles is equal to the cost price of 42 articles.

### Step-by-Step Solution:

1. **Define Variables**:
Let the Selling Price (SP) of one article be \( SP \) and the Cost Price (CP) of one article be \( CP \).

2. **Set Up the Equation**:
According to the problem, the selling price of 39 articles is equal to the cost price of 42 articles. This can be expressed mathematically as:
\[ 39 \times SP = 42 \times CP \]

3. **Express SP in terms of CP**:
Rearranging the equation gives:
\[ SP = \frac{42 \times CP}{39} \]

4. **Simplify the Ratio**:
We can simplify \( \frac{42}{39} \):
\[ SP = \frac{42}{39} \times CP = \frac{14}{13} \times CP \]

5. **Calculate Profit**:
The profit is given by:
\[ \text{Profit} = SP - CP = \left(\frac{14}{13} \times CP\right) - CP \]
To combine the terms, we can express CP as \( \frac{13}{13} \times CP \):
\[ \text{Profit} = \left(\frac{14}{13} - \frac{13}{13}\right) \times CP = \frac{1}{13} \times CP \]

6. **Calculate Profit Percentage**:
The profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{\frac{1}{13} \times CP}{CP}\right) \times 100 \]
Simplifying this gives:
\[ \text{Profit Percentage} = \frac{1}{13} \times 100 = \frac{100}{13} \approx 7.69\% \]

### Final Answer:
The profit percentage is approximately **7.69%**.

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