1. Problem: A shopkeeper buys an article for $200 and sells it for $250. Find the profit and profit percentage. Step 1: Calculate profit using the formula $$\text{Profit} = \text{Selling Price} - \text{Cost Price}$$ Step 2: Substitute the values: $$\text{Profit} = 250 - 200 = 50$$ Step 3: Calculate profit percentage using the formula $$\text{Profit\%} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100$$ Step 4: Substitute the values: $$\text{Profit\%} = \left(\frac{50}{200}\right) \times 100 = 25\%$$ Answer: Profit = $50 and profit percentage = 25%. 2. Problem: A trader sells an article for $600 at a loss of 20%. Find the cost price. Step 1: Use the loss percentage formula $$\text{Loss\%} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100$$ Step 2: Since loss is 20%, selling price is 80% of cost price. So, $$\text{Selling Price} = 0.8 \times \text{Cost Price}$$ Step 3: Substitute selling price as $600: $$600 = 0.8 \times \text{Cost Price}$$ Step 4: Solve for cost price: $$\text{Cost Price} = \frac{600}{0.8} = 750$$ Answer: Cost price = $750. 3. Problem: An article is sold for $900 with a profit of 10%. Find the cost price. Step 1: Sales price = cost price + profit = cost price + 10% of cost price = 1.1 times cost price. Step 2: $$900 = 1.1 \times \text{Cost Price}$$ Step 3: Solve for cost price: $$\text{Cost Price} = \frac{900}{1.1} \approx 818.18$$ Answer: Cost price ≈ $818.18. 4. Problem: A merchant offers a discount of 15% on the marked price of $1000. If the cost price is $850, find the profit or loss. Step 1: Calculate selling price after discount: $$\text{Selling Price} = (1 - 0.15) \times 1000 = 0.85 \times 1000 = 850$$ Step 2: Compare cost price and selling price: both are $850, so no profit or loss. Answer: No profit, no loss. 5. Problem: A shopkeeper sells an article for $1200 after giving a discount of 10%. What is the marked price? Step 1: Selling price = 90% of marked price (because of 10% discount). So, $$1200 = 0.9 \times \text{Marked Price}$$ Step 2: Solve for marked price: $$\text{Marked Price} = \frac{1200}{0.9} = 1333.33$$ Answer: Marked price = $1333.33.