How To Calculate Percentage Profit After Selling An Item At A Discounted Price?
This article will delve into a practical mathematical problem involving calculating percentage profit after a discount. We'll explore the step-by-step process of determining the profit Stella makes after selling a jacket at a discounted price. This is a common scenario in business and retail, making it a valuable concept to understand. So, let’s embark on this mathematical journey to unravel the intricacies of profit calculation in a real-world context.
Understanding the Problem
In this mathematical problem, Stella purchases a jacket for sh. 1800 and intends to sell it at a marked price of sh. 2500. To attract customers during a sale, she offers an 18% discount on the marked price. The objective is to calculate the percentage profit Stella makes after selling the jacket at the discounted price. This problem combines the concepts of cost price, marked price, discount, selling price, and percentage profit. To effectively solve this, we need to understand how these concepts interrelate and apply the appropriate formulas.
- Cost Price: The price at which Stella bought the jacket (sh. 1800).
- Marked Price: The price at which Stella initially intended to sell the jacket (sh. 2500).
- Discount: The reduction offered on the marked price (18%).
- Selling Price: The price at which Stella actually sells the jacket after the discount.
- Profit: The difference between the selling price and the cost price.
- Percentage Profit: The profit expressed as a percentage of the cost price.
Step-by-Step Solution
Calculating the Discount Amount
The first step in determining the percentage profit is to calculate the discount amount. The discount is 18% of the marked price, which is sh. 2500. To calculate this, we multiply the marked price by the discount percentage:
Discount Amount = 18% of sh. 2500
Discount Amount = (18/100) * 2500
Discount Amount = 0. 18 * 2500
Discount Amount = sh. 450
Therefore, the discount amount offered on the jacket is sh. 450. This is the amount by which the marked price will be reduced during the sale.
Determining the Selling Price
Next, we need to calculate the selling price of the jacket after the discount. The selling price is the marked price minus the discount amount:
Selling Price = Marked Price - Discount Amount
Selling Price = sh. 2500 - sh. 450
Selling Price = sh. 2050
So, Stella sells the jacket for sh. 2050 after applying the 18% discount. This is the actual price at which the jacket is sold to the customer.
Calculating the Profit
Now that we have the selling price, we can calculate the profit Stella makes. Profit is the difference between the selling price and the cost price:
Profit = Selling Price - Cost Price
Profit = sh. 2050 - sh. 1800
Profit = sh. 250
Stella makes a profit of sh. 250 on the sale of the jacket. This is the monetary gain she realizes from the transaction.
Calculating the Percentage Profit
Finally, we can calculate the percentage profit. Percentage profit is the profit expressed as a percentage of the cost price:
Percentage Profit = (Profit / Cost Price) * 100
Percentage Profit = (250 / 1800) * 100
Percentage Profit = 0. 138888... * 100
Percentage Profit ≈ 13.89%
Therefore, Stella makes a percentage profit of approximately 13.89% after selling the jacket at the discounted price.
Summarizing the Solution
To recap, we calculated the percentage profit Stella makes after selling the jacket at a discounted price through the following steps:
- Calculated the discount amount: 18% of sh. 2500 = sh. 450.
- Determined the selling price: sh. 2500 - sh. 450 = sh. 2050.
- Calculated the profit: sh. 2050 - sh. 1800 = sh. 250.
- Calculated the percentage profit: (250 / 1800) * 100 ≈ 13.89%.
Thus, Stella makes a percentage profit of approximately 13.89% after selling the jacket at the discounted price. This detailed breakdown illustrates the process of calculating profit in a business scenario involving discounts.
Key Concepts and Formulas Used
To effectively solve this problem, we utilized several key concepts and formulas related to profit and loss. Understanding these concepts is crucial for tackling similar problems in business mathematics.
- Cost Price: The initial price at which an item is purchased.
- Marked Price: The price at which an item is listed for sale before any discounts.
- Discount: A reduction in the marked price, usually expressed as a percentage.
- Selling Price: The final price at which an item is sold after applying any discounts.
- Profit: The gain made from selling an item, calculated as the difference between the selling price and the cost price.
- Percentage Profit: The profit expressed as a percentage of the cost price. This provides a relative measure of profitability.
The key formulas used in this solution are:
- Discount Amount = (Discount Percentage / 100) * Marked Price
- Selling Price = Marked Price - Discount Amount
- Profit = Selling Price - Cost Price
- Percentage Profit = (Profit / Cost Price) * 100
These formulas are fundamental in solving problems related to profit, loss, and discounts. Mastering their application is essential for understanding business transactions and financial calculations.
Real-World Applications
The concepts explored in this problem have numerous real-world applications, particularly in retail and business settings. Understanding how to calculate profit margins and the impact of discounts is crucial for businesses to make informed decisions about pricing and sales strategies.
- Retail Pricing: Retailers use these calculations to determine the optimal selling price for their products. They need to consider the cost price, desired profit margin, and potential discounts to attract customers while maintaining profitability.
- Sales and Promotions: Businesses often offer discounts during sales events to boost sales volume. Calculating the percentage profit after discounts helps them ensure that they are still making a reasonable profit on each sale.
- Inventory Management: Understanding profit margins can help businesses make decisions about which products to stock and how much to order. Products with higher profit margins are often prioritized.
- Financial Analysis: Investors and analysts use profit margin calculations to assess the financial health of a company. A healthy profit margin indicates that a company is managing its costs effectively and generating sufficient revenue.
- Personal Finance: These concepts are also relevant in personal finance. For example, when selling an item online, understanding how to calculate profit after expenses (such as shipping costs) is important.
In summary, the ability to calculate percentage profit after discounts is a valuable skill in various contexts, from running a business to managing personal finances. By understanding these concepts, individuals and organizations can make more informed financial decisions.
Practice Problems
To further solidify your understanding of calculating percentage profit after discounts, let's consider a few practice problems:
Problem 1:
A shopkeeper buys a television for sh. 15,000 and marks it up at sh. 20,000. During a festive sale, he offers a 15% discount. Calculate the percentage profit the shopkeeper makes after the discount.
Problem 2:
Sarah purchases a dress for sh. 1200 and decides to sell it at a marked price of sh. 1800. She offers a 20% discount to her friend. What is the percentage profit Sarah makes?
Problem 3:
A furniture store buys a sofa for sh. 8,000 and marks it at sh. 12,000. If they offer a 10% discount during a clearance sale, calculate the percentage profit the store makes on the sofa.
Solving these problems will help you apply the concepts and formulas discussed earlier. Remember to follow the step-by-step approach: calculate the discount amount, determine the selling price, calculate the profit, and then calculate the percentage profit. These practice problems offer an excellent opportunity to hone your skills in this area.
Conclusion
In conclusion, the problem of calculating percentage profit after a discount is a practical application of mathematical concepts in real-world scenarios. By understanding the relationships between cost price, marked price, discount, selling price, profit, and percentage profit, we can effectively solve such problems. The step-by-step approach outlined in this article provides a clear and concise method for calculating the percentage profit in various situations.
This skill is particularly valuable in business and retail, where pricing strategies and sales promotions play a crucial role in profitability. Mastering these calculations enables businesses to make informed decisions that optimize their financial performance. Moreover, the concepts are also relevant in personal finance, helping individuals make sound decisions when buying or selling items.
By practicing and applying these concepts, you can enhance your mathematical proficiency and gain a deeper understanding of financial transactions. The ability to calculate percentage profit after discounts is a valuable asset in both professional and personal contexts.