Understanding Profit Calculation for Merchandise Sales

Profit calculation can be an essential tool for merchants to assess their business performance. In this article, we will explore an example involving a merchant who sold different portions of his goods at varying profit rates. Let's delve into the detailed steps and methods to calculate the overall profit percentage in such scenarios.

Step-by-Step Calculation for Ratio-Based Profit Distribution

Consider a scenario where a merchant sells 2/3 of his goods at a profit of 20 and the remaining 1/3 at a profit of 14. Our task is to determine the overall profit percentage from the entire sale. Let the total cost of the goods be C. The goods are divided into two parts: The first part comprises 2/3 of the total stock. The second part comprises 1/3 of the total stock. First, we calculate the cost of each part: Cost of the first part: C_1 frac{2}{3}C Cost of the second part: C_2 frac{1}{3}C Next, we calculate the selling price of each part considering their respective profit margins: Selling price of the first part (20% profit): Selling Price_1 1.20 times left(frac{2}{3}Cright) frac{2.4}{3}C Selling price of the second part (14% profit): Selling Price_2 1.14 times left(frac{1}{3}Cright) frac{1.14}{3}C To find the total selling price, we sum up the selling prices of both parts:

Total Selling Price: Selling Price_1 Selling Price_2 left(frac{2.4}{3}Cright) left(frac{1.14}{3}Cright) frac{3.54}{3}C frac{3.54}{3}C

Now, we calculate the overall profit:

Total Cost Price: C

Total Selling Price: frac{3.54}{3}C

Overall Profit: text{Profit} Selling Price - Cost Price frac{3.54}{3}C - C frac{3.54 - 3}{3}C frac{0.54}{3}C

Finally, we determine the overall percentage of profit:

Overall Percentage of Profit: frac{text{Profit}}{C} times 100 frac{0.54/3}{1} times 100 frac{0.54 times 100}{3} 18%

Therefore, the overall percentage of profit is 18%.

Additional Example: Full Goods Sale at a Profit and Cost Price

Here is another example with a different distribution but a similar approach. A merchant sells 3/4 of his goods at a profit of 20 and the remaining 1/4 at cost price. Let C denote the cost price, and S denote the selling price. From the given data, we can derive the following relations: Selling price of 3/4th: S 1 frac{20}{100}times frac{3}{4}C frac{6}{5}times frac{3}{4}C frac{18}{20}C frac{9}{10}C Selling price of 1/4th at cost price: frac{1}{4}C Summing up the selling prices:

Total Selling Price: S left(frac{9}{10}Cright) left(frac{1}{4}Cright) frac{18}{20}C frac{5}{20}C frac{23}{20}C

Now, calculate the overall profit:

Total Cost Price: C

Total Selling Price: frac{23}{20}C

Overall Profit: text{Profit} Selling Price - Cost Price frac{23}{20}C - C frac{23 - 20}{20}C frac{3}{20}C

Determine the overall percentage of profit:

Overall Percentage of Profit: frac{text{Profit}}{C} times 100 frac{3/20}{1} times 100 15%

Therefore, the overall percentage of profit is 15%.

Conclusion

In conclusion, understanding and calculating profit percentages based on different distribution scenarios can provide valuable insights into a merchant's business performance. By applying the methods discussed in this article, merchants can effectively manage their inventory and pricing strategies. This knowledge can help them optimize their sales and increase overall profitability.