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 solve the problem, we need to find the cost price of the item given the marked price, discount, and profit percentage.

1. Understanding the Concepts:

- Marked Price (MP): The original price before discount.
- Discount: Reduction on marked price.
- Selling Price (SP): Price after discount.
- Profit Percentage: Percentage increase over cost price.
- Relationship: \( \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \)

2. Given Values:

- Marked price (MP) = Rs 500
- Discount = 20% → SP = 80% of MP
- Profit = 25%

3. Calculate Selling Price (SP):

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

4. Calculate Cost Price (CP):

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

Final Answer:

The cost price of the item is Rs 320.