A milkman buys pure milk at Rs 24 per litre and adds one fifth of water to it before selling. He then sells the resulting mixture at Rs 32 per litre. What percentage gain does the milkman make on his cost?

Introduction / Context:
This question is about profit computation when a trader adulterates a product by adding water, which is assumed to be free. The milkman buys pure milk and adds water to increase the quantity, then sells the mixture at a higher rate per litre. Many aptitude tests include such problems to check understanding of mixtures, unit cost and effective profit percentage when quantity changes but the cost of the added material is zero.

Given Data / Assumptions:

• Cost price of pure milk = Rs 24 per litre.
• Water is added equal to one fifth of the volume of milk purchased.
• The mixture is sold at Rs 32 per litre.
• Water has zero cost.
• We must find the overall gain percentage on the milkman's cost.

Concept / Approach:
To solve this, assume a convenient initial quantity of milk, say 1 litre. Compute the total volume of the mixture after adding water. Then work out the total cost, which depends only on the milk part, and the total revenue from selling the entire mixture at the given selling price per litre. Finally, compute profit as revenue minus cost and express profit as a percentage of the cost price. The key idea is that free water increases volume, so effective selling price per litre of milk goes up significantly.

Step-by-Step Solution:
Step 1: Assume the milkman buys 1 litre of milk. Cost = 1 * 24 = Rs 24.Step 2: He adds one fifth of water. Water added = 1/5 litre.Step 3: Total volume of mixture = 1 + 1/5 = 6/5 litres = 1.2 litres.Step 4: Since water is free, total cost remains Rs 24.Step 5: Selling price per litre of mixture is Rs 32.Step 6: Total revenue from selling 1.2 litres = 1.2 * 32 = Rs 38.4.Step 7: Profit = Revenue - Cost = 38.4 - 24 = Rs 14.4.Step 8: Profit percentage = (Profit / Cost) * 100 = (14.4 / 24) * 100 = 60%.

Verification / Alternative check:
We can also find effective selling price per litre of pure milk. The milkman sells 1 litre of milk contained in 1.2 litres of mixture for Rs 38.4. Therefore revenue per litre of pure milk is Rs 38.4. Since the cost per litre of pure milk is Rs 24, profit per litre is 38.4 - 24 = 14.4, which again is 60% of 24. This alternate viewpoint confirms the earlier calculation and shows that the milkman gains 60% on his actual money spent.

Why Other Options Are Wrong:
Option A (50%) and option B (40%) are both less than the computed 60% profit and correspond to smaller revenue or larger assumed cost, which do not match the given numbers. Option C (30%) is even further away and clearly incorrect. Only option D, 60, matches the correctly calculated profit percentage when water is added free of cost and the mixture is sold at Rs 32 per litre.

Common Pitfalls:
Students sometimes treat the mixture as if it were still one litre and multiply 32 by 1, forgetting that the milkman now sells 1.2 litres. Another common error is assigning cost to water, which changes the profit percentage and makes the answer wrong. Some also incorrectly apply weighted averages without considering that water adds volume but no cost. Careful attention to quantity and cost of each component is essential in mixture and adulteration questions.

Final Answer:
The milkman makes a 60 percent gain on his cost.