Profit Loss 51B8B7

1. **Problem Statement:** Suppose a shopkeeper buys an article for $100$ and sells it for $120$. We want to find the profit or loss and the profit or loss percentage. 2. **Formulas:** - Profit = Selling Price (SP) - Cost Price (CP) - Loss = Cost Price (CP) - Selling Price (SP) - Profit Percentage = $\frac{\text{Profit}}{\text{Cost Price}} \times 100$% - Loss Percentage = $\frac{\text{Loss}}{\text{Cost Price}} \times 100$% 3. **Step-by-step Solution:** - Given: Cost Price $CP = 100$, Selling Price $SP = 120$ - Calculate Profit: $$\text{Profit} = SP - CP = 120 - 100 = 20$$ - Since $SP > CP$, there is a profit of $20$. - Calculate Profit Percentage: $$\text{Profit Percentage} = \frac{20}{100} \times 100 = 20\%$$ 4. **Explanation:** The shopkeeper made a profit of $20$ which is $20\%$ of the cost price. This means the selling price is $20\%$ more than the cost price. 5. **Additional Example (Loss):** If the shopkeeper sells the article for $80$ instead, then: - Loss = $CP - SP = 100 - 80 = 20$ - Loss Percentage = $\frac{20}{100} \times 100 = 20\%$ So, the shopkeeper incurs a loss of $20$ which is $20\%$ of the cost price. This example helps students understand how to calculate profit, loss, and their percentages clearly.