Question

A shopkeeper allows a discount of 10% on the marked price and still gains 20%; if the marked price is ₹800, what is the cost price?

• A. ₹500
• B. ₹600
• C. ₹650
• D. ₹700

Hint:

Steps for solving discount and profit problems:

• First calculate Selling Price after discount.
• Then apply the profit formula.

Shortcut formula:

SP = MP × (1 − Discount / 100)

SP = CP × (1 + Profit / 100)

Memory trick:

Discount ↓ → SP decreases

Profit ↑ → SP increases

Answer 1

The Correct Option is B

Concept:
In profit and discount problems, three important prices are involved:

• Cost Price (CP) – The price at which the shopkeeper purchases the item.
• Marked Price (MP) – The price printed or listed on the product.
• Selling Price (SP) – The price at which the product is actually sold after giving discount.

The relationships used in such problems are: \[ SP = MP - \text{Discount} \] \[ SP = CP \left(1 + \frac{\text{Profit %}}{100}\right) \]
Step 1: Find the Selling Price after discount.
Marked Price: \[ MP = ₹800 \] Discount given: \[ 10% \text{ of } 800 = 80 \] Selling Price: \[ SP = 800 - 80 = ₹720 \]
Step 2: Use the profit formula.
The shopkeeper gains: \[ 20% \] Thus, \[ SP = CP \left(1 + \frac{20}{100}\right) \] \[ SP = 1.2 \times CP \]
Step 3: Substitute the selling price.
\[ 720 = 1.2 \times CP \] \[ CP = \frac{720}{1.2} \] \[ CP = 600 \]
Step 4: Final answer.
\[ \boxed{₹600} \]