The selling price of 13 articles is same as the cost price of 23 article. What is the profit percentage?

Options

A. `43.47%`
B. `74.83%`
C. `78%`
D. `76.92%`

Answer

To solve the problem step by step, we need to find the profit percentage based on the information given about the selling price (SP) and cost price (CP) of the articles.

### Step 1: Understand the relationship between SP and CP
We are given that the selling price of 13 articles is equal to the cost price of 23 articles. This can be expressed mathematically as:
\[ SP_{13} = CP_{23} \]

### Step 2: Define SP and CP
Let the cost price of one article be \( CP \). Therefore, the cost price of 23 articles is:
\[ CP_{23} = 23 \times CP \]

Let the selling price of one article be \( SP \). Therefore, the selling price of 13 articles is:
\[ SP_{13} = 13 \times SP \]

### Step 3: Set up the equation
From the relationship established in Step 1, we can equate the two expressions:
\[ 13 \times SP = 23 \times CP \]

### Step 4: Express SP in terms of CP
To find the selling price per article in terms of the cost price, we can rearrange the equation:
\[ SP = \frac{23 \times CP}{13} \]

### Step 5: Calculate the profit
The profit can be calculated using the formula:
\[ \text{Profit} = SP - CP \]
Substituting the expression for SP from Step 4:
\[ \text{Profit} = \left(\frac{23 \times CP}{13}\right) - CP \]

To simplify this, we need a common denominator:
\[ \text{Profit} = \frac{23 \times CP}{13} - \frac{13 \times CP}{13} = \frac{(23 - 13) \times CP}{13} = \frac{10 \times CP}{13} \]

### Step 6: Calculate the profit percentage
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the profit from Step 5:
\[ \text{Profit Percentage} = \left(\frac{\frac{10 \times CP}{13}}{CP}\right) \times 100 \]

The \( CP \) cancels out:
\[ \text{Profit Percentage} = \left(\frac{10}{13}\right) \times 100 \]

### Step 7: Calculate the final value
Now, we can calculate the numerical value:
\[ \text{Profit Percentage} = \frac{10 \times 100}{13} \approx 76.92\% \]

### Final Answer
The profit percentage is approximately **76.92%**.

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