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

Options

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

Answer

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

### Step 1: Define Variables
Let the cost price (CP) of 1 article be Rs. X.
Let the selling price (SP) of 1 article be Rs. Y.

### Step 2: Calculate Total Cost Price and Selling Price
- The cost price of 23 articles = 23 * CP = 23 * X = Rs. 23X
- The selling price of 13 articles = 13 * SP = 13 * Y = Rs. 13Y

### Step 3: Set Up the Equation
According to the problem, the selling price of 13 articles is equal to the cost price of 23 articles:
\[ 13Y = 23X \]

### Step 4: Solve for Selling Price in Terms of Cost Price
We can rearrange the equation to express Y in terms of X:
\[ Y = \frac{23X}{13} \]

### Step 5: Calculate Profit
Profit is calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
For 1 article, the profit can be expressed as:
\[ \text{Profit} = Y - X \]
Substituting the value of Y:
\[ \text{Profit} = \frac{23X}{13} - X \]
To combine the terms, we express X as a fraction:
\[ \text{Profit} = \frac{23X}{13} - \frac{13X}{13} = \frac{23X - 13X}{13} = \frac{10X}{13} \]

### Step 6: Calculate Profit Percentage
Profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{10X}{13}}{X} \right) \times 100 \]
The X cancels out:
\[ \text{Profit Percentage} = \left( \frac{10}{13} \right) \times 100 \]

### Step 7: Final Calculation
Now, calculate the profit percentage:
\[ \text{Profit Percentage} = \frac{1000}{13} \approx 76.92\% \]

### Conclusion
The profit percentage is approximately 76.92%.

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