Introduction
The concept of profit and loss is fundamental in business and finance. Understanding how to calculate overall profit or loss after multiple transactions is crucial for any businessperson or investor. This article explores the scenario of selling two items at a loss and profit, respectively, and determining the net profit or loss. We'll delve into the calculation methods, provide detailed examples, and explain the underlying principles to help you apply this knowledge effectively.
The Scenario
We are given the scenario where a seller sells two TV sets. The first TV set is sold at a loss of 10%, while the second TV set is sold at a profit of 10%. The question is to determine if there is a net profit or loss after these transactions and to calculate the overall percentage change.
Step-by-Step Calculation
Assumption: Let the cost price (CP) of each TV set be 100.
Selling Price (SP) Calculations:
First TV Set (Loss 10%): Loss 10% of CP 10 SP CP - Loss 100 - 10 90 Second TV Set (Profit 10%): Profit 10% of CP 10 SP CP Profit 100 10 110Total Cost Price (CP):
Total CP 100 100 200
Total Selling Price (SP):
Total SP 90 110 200
Overall Profit or Loss Calculation
Total SP - Total CP 200 - 200 0
Since the result is 0, we conclude that there is no net profit or loss in the overall transaction. The overall percentage change is also 0.General Formula for Profit and Loss
Let's explore a more generalized approach to calculate overall profit or loss when selling items at different percentages of profit or loss.
General Case
Assumptions:
Cost Price of Item 1 (CP1) Cost Price of Item 2 (CP2) 100 Selling Price of Item 1 (SP1) with a 10% loss SP1 90 Selling Price of Item 2 (SP2) with a 10% profit SP2 110Total CP:
Total CP CP1 CP2 100 100 200
Total SP:
Total SP SP1 SP2 90 110 200
Overall Profit or Loss:
Total SP - Total CP 0
Hence, there is no net profit or loss in the overall transaction.
Additional Examples
Example 1
Assumptions:
CP1 CP2 100 SP1 with a 15% loss SP1 85 SP2 with a 15% profit SP2 115Total CP:
Total CP CP1 CP2 100 100 200
Total SP:
Total SP SP1 SP2 85 115 200
Overall Profit or Loss:
Total SP - Total CP 0
Conclusion: There is no net profit or loss.
Example 2
Given: Selling each TV set at Rs. 15,000.
Selling at a 10% loss: SP1 15000 Selling at a 15% profit: SP2 15000Calculations:
CP1 15000 / (100 - 10) * 100 15000 / 90 * 100 16666.67
CP2 15000 / (100 15) * 100 15000 / 115 * 100 13043.48
Total CP (CP1 CP2): 16666.67 13043.48 29710.15
Total SP (SP1 SP2): 15000 15000 30000
Profit: 30000 - 29710.15 289.85
Conclusion
In all the examples provided, we calculated the overall profit or loss after selling items at various percentages of profit or loss. In each case, the overall result was zero, indicating no net profit or loss. This method can be applied to any similar scenario to determine if a sale results in a net profit or loss.