A person buys an article for some rupees. He finds that if he had sold the article at a profit of `13% `of the selling price rather than selling it at a profit of `13%` of the cost price then he would have got ₹422.50 more. Find the cost price of the article.

Options

A. ₹ 42250
B. ₹ 52000
C. ₹ 27300
D. ₹ 25000

Answer

To solve the problem, we need to find the cost price of the article based on the information provided. Let's break it down step by step.

### Step 1: Define the Variables
Let the cost price of the article be \( CP = 100x \) rupees.

### Step 2: Calculate Selling Price at 13% Profit on Cost Price
When sold at a profit of 13% on the cost price, the selling price \( SP_1 \) can be calculated as follows:
\[ SP_1 = CP + 13\% \text{ of } CP = 100x + \frac{13}{100} \times 100x = 100x + 13x = 113x \text{ rupees} \]

### Step 3: Calculate Profit when Selling Price is Based on Selling Price
If the article is sold at a profit of 13% on the selling price, the profit \( P_2 \) can be calculated as:
\[ P_2 = 13\% \text{ of } SP_1 = \frac{13}{100} \times 113x = \frac{1469x}{100} = 14.69x \text{ rupees} \]

### Step 4: Calculate Profit when Selling Price is Based on Cost Price
The profit \( P_1 \) when sold at a profit of 13% on the cost price is:
\[ P_1 = 13\% \text{ of } CP = \frac{13}{100} \times 100x = 13x \text{ rupees} \]

### Step 5: Set Up the Equation Based on the Given Information
According to the problem, the difference between the two profits is given as ₹422.50:
\[ P_2 - P_1 = 422.50 \]
Substituting the values of \( P_2 \) and \( P_1 \):
\[ 14.69x - 13x = 422.50 \]
This simplifies to:
\[ 1.69x = 422.50 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{422.50}{1.69} \]
Calculating this gives:
\[ x \approx 250 \text{ rupees} \]

### Step 7: Calculate the Cost Price
Now, substituting the value of \( x \) back into the cost price:
\[ CP = 100x = 100 \times 250 = 25000 \text{ rupees} \]

### Final Answer
The cost price of the article is ₹25,000.

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