Profit Calculation in Retail: Discount and Cost Price Analysis

Introduction

In the world of retail, understanding the relationship between the cost price (CP), marked price (MP), and selling price (SP) is crucial for making a profit. This article will guide you through the step-by-step process of calculating the actual cost of an article given a discount and the resulting profit. We will also explore how similar calculations can be applied to other retail scenarios.

Calculating the Cost Price Given a Discount and Marked Price

Consider an example where a shopkeeper offers a 20% discount on an article marked at Rs 300, and still makes a 20% profit. To find the actual cost of the article, follow these steps:

Step 1: Determine the Selling Price after the Discount

- Marked Price (MP) Rs 300 - Discount offered 20% - Discount 20% of Rs 300 Mathematically, this is calculated as: [text{Discount} frac{20}{100} times 300 Rs 60] - Selling Price (SP) after discount Marked Price - Discount [text{SP} 300 - 60 Rs 240]

Step 2: Relate the Selling Price to the Cost Price

- The shopkeeper makes a 20% profit on the cost price (CP). - If the profit is 20%, the selling price can be expressed as: [text{SP} text{CP} times (1 text{Profit}) 1.20 times text{CP}] Given that SP Rs 240, we can solve for CP: [1.20 times text{CP} 240] [text{CP} frac{240}{1.20} Rs 200] Thus, the actual cost of the article is **Rs 200**.

Additional Scenarios

Scenario 1: Another Example with a 10% Discount

For an article costing Rs 450, let's apply the same logic to calculate the marked price (MP) given that the shopkeeper gives a 10% discount and still makes a 20% profit. - Let (M) denote the required marked price of the given article. - SP after 10% discount 90% of MP - [text{SP} frac{90}{100} M] - SP with 20% profit 120% of CP 120% of Rs 450 - [text{SP} frac{120}{100} times 450 Rs 540] - Therefore, - [frac{90}{100} M 540] - Solving for (M) we get: - [M frac{540 times 100}{90} Rs 600] - Hence, the marked price is **Rs 600**.

Scenario 2: Another Approach Using Ratios

As another example, let's consider a cost price (CP) of Rs 100 and a selling price (SP) after a 10% discount of Rs 90. If the profit is 20%, the selling price after discount is Rs 120. We can use ratios to find the marked price (MP): - CP 100 - Profit 20% 20 - SP CP Profit 120 - MP [frac{120}{100} times 90 400/3] - If CP 100, then MP (400/3) - If CP 450, then MP (400/3 times frac{450}{100} 600) - Hence, the marked price is **Rs 600**.

Calculating Marked Price Given SP and Discount

Consider an article that is sold for Rs 357 with a 15% discount. We want to find the marked price (MP) when the shopkeeper made a 5% profit on the cost price of Rs 340. - Cost price (CP) Rs 340 - Profit 5% of CP 5/100 times 340 Rs 17 - Selling price (SP) CP Profit Rs 357 - After a 15% discount, MP SP / (1 - Discount) - MP (357 / (1 - 0.15) 357 / 0.85 Rs 420) - Hence, the marked price is **Rs 420**.

Conclusion

Understanding the relationship between selling price, cost price, and marked price is fundamental for retail businesses. This article has demonstrated how to calculate these values step-by-step. Whether you are a shopkeeper or a business owner, mastering these calculations is crucial for maximizing profits while offering appealing discounts to customers.

Keywords: retail profit calculation, cost price calculation, discount and markup analysis