A milkman cheats his customer in two ways. He mixes 10% water in pure milk and increases the price of milk by 10%. He purchases 20 kg pure milk at a rate of ₹ 15 per kg. His total profit by selling it is (Hotel Management, 2007)

### Concept & Double Profit Mechanism When a merchant increases volume with a free substitute (water) and also raises the markup on the selling price, the final revenue is calculated on the total adulterated quantity multiplied by the new rate. $$Total\ Profit = Total\ Revenue - Total\ Cost$$ ### Step-by-Step Solution * **Total Cost Price (CP):** The milkman buys 20 kg of pure milk at ₹ 15 per kg. * $Total\ CP = 20 \times 15 = 300$. * **Adulteration:** He mixes 10% water into the 20 kg of milk. * Water added = $10\%$ of $20 = 2$ kg. * Total volume to sell = $20 + 2 = 22$ kg. * **Price Markup:** He increases the selling price by 10% over his cost rate (₹ 15). * New Selling Price (SP) rate = $15 + (10\%$ of $15) = 15 + 1.50 = 16.50$ per kg. * **Total Revenue:** $22 \times 16.50 = 363$. * **Total Profit:** $Total\ SP - Total\ CP = 363 - 300 = 63$. ### Exam Strategy & Shortcut Instead of calculating absolute totals first, you can use successive percentage changes on the volume and price. Volume increases by 10% (multiplier 1.1) and price increases by 10% (multiplier 1.1). Total revenue multiplier = $1.1 \times 1.1 = 1.21$. This means a 21% overall profit on the initial cost. Profit = $21\%$ of $300 = 63$. ### Common Pitfall A common mistake is adding the two 10% cheats linearly ($10\% + 10\% = 20\%$) to get a 20% profit on ₹ 300, which yields ₹ 60, an incorrect but tempting trap. ### Final Answer Therefore, the correct answer is **₹ 63**.