Understanding Marked Price and Discount

This problem involves finding the original price (marked price) of an item when you know the price it was sold for (selling price) and the percentage discount given.

• Selling Price (SP): The price at which the shopkeeper sold the pen.
• Discount: A reduction in price given by the seller.
• Marked Price (MP): The price originally labeled on the item before any discount is applied.

The relationship between these is: Selling Price = Marked Price - Discount Amount.

The discount amount is calculated based on the Marked Price. Specifically, Discount Amount = Discount Percentage × Marked Price.

Calculating the Marked Price

Here's how to calculate the marked price step-by-step:

1. Identify the given information:
   • Selling Price (SP) = Rs. 45
   • Discount Percentage = 10%
2. Understand the discount effect: A 10% discount means the customer pays 100% - 10% = 90% of the marked price.
3. State the formula:

   We can express the selling price in terms of the marked price and discount percentage:

   $ \text{SP} = \text{MP} \times (1 - \text{Discount Percentage}) $

4. Substitute the known values into the formula:

   Let the Marked Price be MP.

   $ \text{Rs. } 45 = \text{MP} \times (1 - 10\%) $

   Convert the percentage to a decimal:

   $ 10\% = \frac{10}{100} = 0.10 $

   So the equation becomes:

   $ \text{Rs. } 45 = \text{MP} \times (1 - 0.10) $

5. Simplify and solve for the Marked Price (MP):

   $ \text{Rs. } 45 = \text{MP} \times (0.90) $

   To find MP, divide the Selling Price by 0.90:

   $ \text{MP} = \frac{\text{Rs. } 45}{0.90} $

   $ \text{MP} = \frac{450}{9} $

   $ \text{MP} = \text{Rs. } 50 $

Therefore, the marked price of the pen was Rs. 50.