Introduction

When selling an item, the dynamics between its cost price, marked price, and sale price play a crucial role in determining the profit or loss percent. This article will explore how to calculate the profit or loss percent made on an item, given a specific marked price and discount. We will provide detailed steps and examples to illustrate the process.

Calculating Profit Percent When Marked 60 Percent Above Cost Price and Sold at 20 Percent Discount

Let's consider an example where an article is marked 60 percent above its cost price and sold at a 20 percent discount. We aim to determine the profit percent made.

Step-by-Step Calculation

Define Variables: C: Cost Price
MP: Marked Price
SP: Selling Price
P: Profit Percentage Given Data: Marked Price (MP) 160% of Cost Price (C) 1.60C
Discount 20%
Selling Price (SP) MP - (Discount * MP) 1.60C - (0.20 * 1.60C) 1.60C - 0.32C 1.28C Profit Calculation:

Profit Percentage (P) (SP - C) / C * 100
P (1.28C - C) / C * 100
P 0.28C / C * 100
P 28%

Profit or Loss Percent Calculation Using Marked Price

Another scenario involves finding the required discount to achieve a specific profit percentage. Let's solve this problem step-by-step.

Problem Statement

An item's marked price is 50 percent above its cost price. What discount percentage is needed to achieve a 10 percent profit?

Step-by-Step Solution

Define Variables: C: Cost Price
MP: Marked Price
SP: Selling Price
D: Discount
P: Profit Percentage Given Data: Marked Price (MP) 150% of Cost Price (C) 1.50C
Required Profit (P) 10% 0.10C
Selling Price (SP) MP - (Discount * MP) 1.50C - 1.50C * D 1.50C - 1.50CD
Profit Calculation:

P (SP - C) / C * 100
0.10C (1.50C - 1.50CD - C) / C * 100
0.10C (0.50C - 1.50CD) / C * 100
0.10C (0.50 - 1.50D) * 100
0.10 0.50 - 1.50D
1.50D 0.40
D 0.40 / 1.50 0.266666 26.66667%

Practical Application: Marked 60 Percent Above CP

Consider an article initially marked 60% above its cost price and then sold at a 20% discount. Let's compute the profit percent in this scenario.

Calculation

Define Variables: C: Cost Price
MP: Marked Price 160% of C 1.60C
SP: Selling Price 80% of MP 0.80 * 1.60C 1.28C
Profit Calculation:

Profit Percentage (P) (SP - C) / C * 100
P (1.28C - C) / C * 100
P 0.28C / C * 100
P 28%

Conclusion

In conclusion, whether you are simplifying the calculation process or dealing with more complex scenarios, understanding the relationship between cost price, marked price, and selling price is crucial for determining profit or loss percentages.

Always ensure to verify input data and follow structured calculations to avoid common arithmetic errors.