Finding the Optimal Selling Price for Profit

Introduction

Selling an item at a specified price can result in a loss or a profit. Understanding how to calculate the cost price and the selling price for a desired profit margin is crucial in business. This article will guide you through determining the selling price that will yield a specific profit based on the cost price and the loss incurred on a previous transaction.

Calculating the Cost Price

In the first scenario, a man sells an article for 265 Rs and incurs a loss of 15%. To find the cost price (CP), we use the formula:

Selling Price (SP) Cost Price (CP) × (1 - (Loss % / 100))

Given:

SP 265 Rs Loss 15%

Substituting the values into the formula:

265 CP × (1 - 0.15)

265 CP × 0.85

CP 265 / 0.85 ≈ 311.76 Rs

Calculating the Selling Price for a Desired Profit

To find the selling price for a desired profit of 20%, we use the formula:

Selling Price (SP) Cost Price (CP) × (1 (Profit % / 100))

Given:

CP 311.76 Rs Profit 20%

Substituting the values into the formula:

SP 311.76 × 1.20 ≈ 374.11 Rs

Thus, the man should sell the article for approximately 374.11 Rs to make a profit of 20%.

Solving Related Problems

Let's work through a related example. If the cost price is 250 Rs and a loss of 40% is incurred, the actual selling price is found as follows:

SP 250 × (1 - (40 / 100)) 250 × 0.60 150 Rs

To make a profit of 20%, the selling price should be:

SP 250 × (1 (20 / 100)) 250 × 1.20 300 Rs

Advanced Example

For a more complex example, let's consider an item sold for 300 Rs resulting in a 20% loss. We need to find the cost price first:

CP × (1 - (20 / 100)) 300

CP × 0.80 300

CP 300 / 0.80 375 Rs

To achieve a 25% profit, the selling price should be:

SP 375 × (1 (25 / 100)) 375 × 1.25 468.75 Rs

Thus, the item should be sold for 468.75 Rs to make a 25% profit.

Conclusion

Understanding how to calculate the cost price and the selling price for a desired profit is essential in business. By using the appropriate formulas for cost and selling prices, one can optimize pricing strategies to maximize profits and minimize losses.