Question

A shopkeeper sells an item at a 20 % discount on the marked price and still makes a 25 % profit. If the marked price is 500 rupees, what is the cost price of the item?

• A. 300 rupees
• B. 320 rupees
• C. 350 rupees
• D. 400 rupees

Hint:

For discount and profit problems, calculate the selling price using the discount percentage, then use the profit percentage to find the cost price with \( \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit\%}}{100}} \).

Answer 1

The Correct Option is B

To determine the item's cost price, we must use the marked price, discount percentage, and profit percentage.

1. Key Definitions:

- Marked Price (MP): The initial price before any reduction.
- Discount: The amount subtracted from the marked price.
- Selling Price (SP): The final price after the discount is applied.
- Profit Percentage: The percentage increase relative to the cost price.
- Formula: \( \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \)

2. Provided Information:

- Marked price (MP) = Rs 500
- Discount = 20%. This means the Selling Price is 80% of the Marked Price.
- Profit = 25%

3. Selling Price Calculation:

\[ \text{SP} = 0.8 \times 500 = 400 \]

4. Cost Price Calculation:

\[ 400 = \text{CP} \times \left(1 + \frac{25}{100}\right) = \text{CP} \times 1.25 \] \[ \text{CP} = \frac{400}{1.25} = 320 \]

Conclusion:

The item's cost price is Rs 320.