Lecture on Application of Percentages: Profit and Loss

Key Concepts

• Cost Price (CP): The price at which an item is purchased.
• Selling Price (SP): The price at which an item is sold.
• Profit: Occurs when SP > CP. Calculated as Profit = SP - CP.
• Loss: Occurs when SP < CP. Calculated as Loss = CP - SP.
• Profit Percentage: Profit % = (Profit / CP) * 100
• Loss Percentage: Loss % = (Loss / CP) * 100

Formulas

Profit

• Profit Calculation: Profit = SP - CP
• Profit Percent: Profit % = (Profit / CP) * 100
• Cost Price from Profit Percent: CP = 100 / (100 + Profit%) * SP
• Selling Price from Profit Percent: SP = (100 + Profit%) / 100 * CP

Loss

• Loss Calculation: Loss = CP - SP
• Loss Percent: Loss % = (Loss / CP) * 100
• Cost Price from Loss Percent: CP = 100 / (100 - Loss%) * SP
• Selling Price from Loss Percent: SP = (100 - Loss%) / 100 * CP

Examples

Example 1: Rice Sale

• Selling 5 cups for: 2 Ghana Cedis
• Profit per cup: 8 Ghana Pesos
  • Convert 8 Pesos to Cedis: 0.08 Ghana Cedis
  • Total profit for 5 cups: 0.08 * 5 = 0.40 Ghana Cedis
• Cost Price Calculation:
  • CP = 2 - 0.40 = 1.60 Ghana Cedis
• Profit Percent Calculation:
  • Profit % = (0.40 / 1.60) * 100 = 25%

Example 2: Article Sale

• Selling Price: 4 Ghana Cedis
• Profit Percent: 25%
• Cost Price Calculation using Ratio and Proportion:
  • CP = (4 * 100) / 125 = 3.20 Ghana Cedis
• Profit Calculation:
  • Profit = 4 - 3.20 = 0.80 Ghana Cedis (or 80 Pesos)

Example 3: Land Sale

• Cost Price: 4,800 Ghana Cedis
• Selling Price: 4,000 Ghana Cedis
• Loss Calculation:
  • Loss = 4,800 - 4,000 = 800 Ghana Cedis
• Loss Percent Calculation:
  • Loss % = (800 / 4,800) * 100 = 16.67%

Conclusion

• Understanding these basic concepts of profit and loss, and the ability to calculate percentages is crucial for financial literacy.
• Always remember to fix the cost price at the denominator when calculating percentages.

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