Understanding Marked Price Calculation

This problem asks us to find the original marked price of an article. We know the selling price after a certain discount percentage was applied.

Key Information Provided

• Discount Percentage: 13%
• Selling Price (SP): ₹348
• Goal: Find the Marked Price (MP)

Formula for Discount

The relationship between Selling Price (SP), Marked Price (MP), and Discount Percentage is given by the formula:

$ SP = MP \times \left(1 - \frac{\text{Discount}\%}{100}\right) $

Alternatively, this can be written as:

$ SP = MP \times \left(\frac{100 - \text{Discount}\%}{100}\right) $

Step-by-Step Calculation

1. Identify the known values:

   • SP = ₹348
   • Discount% = 13

2. Substitute the values into the formula:

   $ ₹348 = MP \times \left(\frac{100 - 13}{100}\right) $

3. Simplify the expression in the parenthesis:

   $ ₹348 = MP \times \left(\frac{87}{100}\right) $

4. Rearrange the formula to solve for MP:

   $ MP = ₹348 \times \left(\frac{100}{87}\right) $

5. Perform the calculation:

   $ MP = \frac{₹348 \times 100}{87} $

   First, divide 348 by 87:

   $ \frac{348}{87} = 4 $

   Now, multiply the result by 100:

   $ MP = 4 \times 100 $

   $ MP = ₹400 $

Verification of the Marked Price

Let's check if a marked price of ₹400 with a 13% discount results in a selling price of ₹348.

• Marked Price (MP) = ₹400
• Discount = 13% of ₹400
• Discount Amount = $ \frac{13}{100} \times 400 = 13 \times 4 = ₹52 $
• Selling Price (SP) = MP - Discount Amount
• SP = ₹400 - ₹52 = ₹348

The calculated selling price matches the given selling price, confirming our marked price is correct.

Conclusion

The marked price of the article is ₹400.