Profit Percentage Calculation Post Discount on Marked Price

Understanding how discounts affect profit percentages is crucial for shopkeepers and business owners. This article explores the scenario where a shopkeeper makes a profit of 20% even after providing a discount of 10% on the marked price and then calculates the profit percentage if a 20% discount is applied. Let's break down the problem step-by-step and explore the underlying mathematical principles.

Initial Profit Calculation with 10% Discount

Let's assume the cost price (CP) of the good is X.

Step 1: Calculate the Marked Price (MP)

The marked price (MP) represents the price at which the item is first listed for sale. In this scenario, the marked price is increased by 20%, so:

MP X 20% of X 1.2X

Step 2: Selling Price After 10% Discount

When a 10% discount is provided, the selling price (SP) becomes:

SP MP - 10% of MP 1.2X - 0.1(1.2X) 1.2X - 0.12X 1.08X

The gain or profit is the difference between the selling price and the cost price:

Profit SP - CP 1.08X - X 0.08X

The profit percentage is then calculated as:

Profit Percentage (Profit / CP) * 100 (0.08X / X) * 100 8%

Detailed Calculation for Specific Cost Price

Let's assume the cost price (CP) of the item is Rs. 100.

Step 1: Calculate the Marked Price (MP)

If the cost price is Rs. 100, then the marked price (MP) is:

MP 100 20% of 100 120

Step 2: Apply a 10% Discount

When a 10% discount is applied to the marked price, the new selling price (SP) is:

SP 120 - 10% of 120 120 - 12 108

The profit is:

Profit SP - CP 108 - 100 8

This confirms that with a 10% discount, the profit is Rs. 8.

New Scenario with 20% Discount

Let's now consider the situation where the shopkeeper provides a 20% discount on the marked price.

Step 1: Express the Marked Price (MP) in Terms of Cost Price (CP)

Let the cost price (CP) of the goods be Rs. x. Then, the marked price (MP) will be:

MP x 20% of x 1.2x

Step 2: Selling Price After 20% Discount

When a 20% discount is applied to the marked price, the new selling price (SP) will be:

SP MP - 20% of MP 1.2x - 0.2(1.2x) 1.2x - 0.24x 0.96x

Step 3: Calculate the Profit

The profit when selling at this new selling price is:

Profit SP - CP 0.96x - x -0.04x

Since the cost price is Rs. x, the profit percentage is:

Profit Percentage (Profit / CP) * 100 (-0.04x / x) * 100 -4%

This calculation shows that providing a 20% discount would result in a loss, not a profit.

Practical Application

In the example given, let's take the cost price (CP) to be Rs. 10:

Step 1: Marked Price (MP)

Marked Price (MP) 10 20% of 10 12

Step 2: Selling Price After 20% Discount

Selling Price (SP) 12 - 20% of 12 12 - 2.4 9.6

The profit is:

Profit SP - CP 9.6 - 10 -0.4

Therefore, the loss is Rs. 0.4, and the loss percentage is:

Loss Percentage (Loss / CP) * 100 (-0.4 / 10) * 100 -4%

Conclusion

Based on the calculations, if the shopkeeper provides a discount of 20% on the marked price, the profit percentage will be -4%, indicating a loss rather than a profit. This emphasizes the importance of accurate pricing and discount management in maintaining profitability.