The formula for Cost Price (CP) depends on what information you have available, primarily whether you know the Selling Price (SP) and either the Profit Percentage or the Loss Percentage.
Formulas for Calculating Cost Price (CP)
Here are the common formulas used to calculate the Cost Price:
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When Selling Price (SP) and Profit Percentage are known:
CP = {100 / (100 + Profit%)} × SP
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When Selling Price (SP) and Loss Percentage are known:
CP = {100 / (100 – Loss%)} × SP
Explanation of the Formulas
The core concept behind these formulas is to reverse the calculations that determine profit or loss. Profit and loss are always calculated based on the cost price.
- Profit: Selling Price (SP) - Cost Price (CP)
- Loss: Cost Price (CP) - Selling Price (SP)
- Profit %: (Profit / CP) × 100
- Loss %: (Loss / CP) × 100
The formulas provided effectively isolate CP when you already know the SP and the percentage gain or loss.
Examples
Here are examples using each formula:
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Example 1: Profit A product sells for $150 (SP) and generates a profit of 20%. What is the Cost Price?
CP = {100 / (100 + 20)} × $150
CP = {100 / 120} × $150
CP = 0.8333 × $150
CP = $125 -
Example 2: Loss A product sells for $80 (SP) and incurs a loss of 10%. What is the Cost Price?
CP = {100 / (100 - 10)} × $80
CP = {100 / 90} × $80
CP = 1.1111 × $80
CP = $88.89 (approximately)
Conclusion
In summary, there isn't just one formula for CP; it depends on the context. If you know the selling price and either the profit or loss percentage, you can use the formulas above to calculate the cost price.
