A milkman has 20 litres of pure milk and adds 5 litres of free water to it; if the cost price of pure milk is Rs. 18 per litre and he sells the entire 25 litre mixture at Rs. 18 per litre, what is his profit percentage?

Introduction / Context:
This is another classic mixture and profit question involving adulteration with water. The milkman increases the volume of what he sells by mixing water, which has no cost. He still charges the same rate per litre as for pure milk. Such scenarios are common in aptitude tests to check whether the learner can correctly separate cost bearing components from free components and then compute the resulting profit percentage.

Given Data / Assumptions:

• Initial quantity of pure milk = 20 litres.
• Quantity of water added = 5 litres.
• Total quantity after mixing = 25 litres.
• Cost price of pure milk per litre = Rs. 18.
• Water is free and does not add to the cost.
• The mixture of 25 litres is sold at Rs. 18 per litre.
• We need to find the profit percentage on the milkman cost.

Concept / Approach:
The milkman pays only for the milk, not for the water. Profit arises because he sells more litres than he actually paid for. First, find the total cost of the milk. Then, calculate the total selling price of the mixture. The difference between total selling price and total cost gives the profit in rupees. Finally compute profit percentage using profit divided by cost price multiplied by 100. This is the standard approach in adulteration type questions.

Step-by-Step Solution:
Step 1: Cost price of 1 litre of milk = Rs. 18.Step 2: Quantity of milk = 20 litres.Step 3: Total cost of milk = 20 * 18 = Rs. 360.Step 4: Quantity of water added = 5 litres, cost of water = Rs. 0.Step 5: Total mixture quantity = 20 + 5 = 25 litres.Step 6: Selling price per litre of mixture = Rs. 18.Step 7: Total selling price = 25 * 18 = Rs. 450.Step 8: Profit = 450 - 360 = Rs. 90.Step 9: Profit percentage = (Profit / Cost price) * 100.Step 10: Profit percentage = (90 / 360) * 100.Step 11: Simplify 90 / 360 = 1 / 4, so profit percentage = 25%.

Verification / Alternative check:
An intuitive way to confirm is to consider that the milkman paid for only 20 litres but sells 25 litres. Free extra litres = 5. The free quantity as a fraction of the original paid quantity is 5 / 20 = 1 / 4. Therefore, the gain on cost is 25%. This matches the detailed calculation, confirming the correctness of the result.

Why Other Options Are Wrong:

• 20%: This would imply that free quantity is one fifth of the paid quantity, which is not true here because 5 is not one fifth of 20.
• 33.33%: That suggests a free quantity equal to one third of cost basis. However 5 is not one third of 20.
• 18%: This is unrelated to the ratio of free quantity to paid quantity and does not match the computed profit.

Common Pitfalls:

• Using the total quantity 25 litres as the cost base instead of the original 20 litres paid for.
• Thinking that selling at cost price per litre always gives zero profit, ignoring the effect of added free water.
• Confusing absolute profit in rupees with profit percentage on cost.

Final Answer:
The milkman earns a profit of 25% by mixing water and selling the mixture at the original cost price per litre.