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

Step 1: Understanding the Question:

The question provides the Marked Price (MP), discount percentage, and gain percentage. We need to find the Cost Price (CP).

Step 2: Key Formula or Approach:

1. Calculate the Selling Price (SP) using the Marked Price and Discount.
SP = MP × (1 − Discount% / 100)

2. Use the Selling Price and Gain percentage to find the Cost Price.
SP = CP × (1 + Gain% / 100)

Alternatively, a direct formula relating CP and MP is:
CP / MP = (100 − Discount%) / (100 + Gain%)

Step 3: Detailed Explanation:

Method 1: Step-by-step calculation

Given: Marked Price (MP) = ₹800, Discount = 10%, Gain = 20%.

First, calculate the Selling Price (SP).
Discount Amount = 10% of 800 = (10 / 100) × 800 = ₹80
SP = MP − Discount Amount = 800 − 80 = ₹720

Now, we know the shopkeeper gains 20% on the Cost Price (CP).
This means SP is 120% of CP.
SP = CP × (1 + 20/100) = CP × 1.2
720 = CP × 1.2
CP = 720 / 1.2 = ₹600

Method 2: Using the direct formula

CP / 800 = (100 − 10) / (100 + 20)
CP / 800 = 90 / 120 = 3 / 4
CP = 800 × (3 / 4)
CP = ₹600

Step 4: Final Answer:

The cost price of the item is ₹600.