Calculating Profit Percentages Using Given Loss in an Article’s Selling Price
Understanding the relationship between the cost price, selling price, and profit margin is crucial in the retail and sales industries. This article will guide you through several scenarios involving the sale of an article at different prices and how to calculate the resulting profit percentage, given a specific loss at a lower selling price.
Scenario 1: Selling an Article at 2/3rds the Price Results in a 20% Loss
Let the selling price be x. If the article is sold at 2/3rd of the original selling price, a loss of 20% would be incurred. Here's how to find the profit percentage if the article is sold at its original price:
Step 1: Determine the cost price (CP) from the given loss.
Given: Selling price at 2/3rd of x results in a loss of 20%. Therefore, the equation for cost price is:
CP (4/5) * (x / (1 - 0.20)) (4/5) * (x / 0.80) 8x/9.
Step 2: Calculate the profit.
Profit Original selling price - Cost price x - 8x/9 x/9.
Step 3: Determine the profit percentage.
Profit percentage (Profit / CP) * 100 (x/9) / (8x/9) * 100 25/2 12 1/2%.
Scenario 2: Selling at 3/4rd the Price Results in a 10% Loss
Let the selling price be x. If the article is sold at 3/4th of the original selling price, a loss of 10% would be incurred. Here’s the calculation for the profit percentage:
Step 1: Determine the cost price (CP).
New selling price 3x/4. Given a loss of 10%, the equation for CP is:
CP (100 * 3x/4) / (1 0.10) (100 * 3x/4) / 1.10 5x/6.
Step 2: Calculate the profit.
Profit Original selling price - Cost price x - 5x/6 x/6.
Step 3: Determine the profit percentage.
Profit percentage (100 * Profit / CP) (100 * x/6) / (5x/6) * 100 20%.
Scenario 3: Determining Profit When Selling at Halved Price Results in a 35 Loss
Let the previous selling price be 10. If the article is sold at half of the previous selling price, a loss of 35 would be incurred. Here’s how to find the profit percentage:
Step 1: Determine the cost price (CP).
Loss 35 at 1/2 of SP. Therefore, SP 10 and CP at 1/2 of SP is given by:
CP (100 * 10) / (1 (35/10)) (100 * 10) / 210 100/21 ≈ 77/13.
Step 2: Calculate the profit.
Profit Original selling price - Cost price 10 - 77/13 ≈ 23/13 ≈ 23/77 * 100 ≈ 30%.
Scenario 4: Determining Profit When Selling at 2/3rds the Price Results in a 25% Loss
Let the original selling price be x. If the article is sold at 2/3rds of the original selling price, a loss of 25% would be incurred. Here’s the calculation for the profit percentage:
Step 1: Determine the cost price (CP).
Loss 25%. Therefore, the equation for CP is:
3/5 * x CP / (1 - 0.25) 0.8x.
Step 2: Calculate the profit.
Profit Original selling price - Cost price x - 0.8x 0.2x.
Step 3: Determine the profit percentage.
Profit percentage (0.2x / 0.8x) * 100 25%.
Scenario 5: Determining Profit When Selling at 2/3rds the Price Results in a 10% Loss
Let the marked price be x. If the article is sold at 2/3rds of the marked price, a loss of 20 is incurred. Here’s the calculation for the profit percentage:
Step 1: Determine the cost price (CP).
SP at 2/3 of x 2x/3. CP can be found as:
CP (2x/3) / (1 0.20) (2x/3) / 1.20 2x/3.60 20/270.
Step 2: Calculate the profit.
Profit Original selling price - CP x - 20/270 7/270.
Step 3: Determine the profit percentage.
Profit percentage (7/270 / 20/270) * 100 35%.
Conclusion
By understanding these scenarios, you can calculate the profit percentage accurately, which is crucial for effective pricing and sales strategies. Whether using algebraic equations or logical deductions, these calculations can provide insight into the profitability of different pricing strategies. The key is to clearly define the cost price and selling price in each scenario before performing the necessary calculations.