A milkman has 20 litres of pure milk and mixes 5 litres of free water into it; if the cost price of pure milk is Rs. 18 per litre, then what percentage profit does he earn by selling the entire 25 litre mixture at the same cost price per litre?

Introduction / Context:
This aptitude question on profit and loss deals with adulteration, where a milkman mixes free water into pure milk and then sells the diluted mixture at the original cost price of milk. Problems of this type test understanding of cost price, selling price, effective quantity, and how mixing a free component like water increases profit percentage without changing the nominal selling price per litre.

Given Data / Assumptions:

• The milkman initially has 20 litres of pure milk.
• He mixes 5 litres of water into the milk, and water is assumed to be free of cost.
• The cost price of pure milk is Rs. 18 per litre.
• He sells the entire mixture at Rs. 18 per litre, that is, at the original cost price of pure milk.
• There is no extra cost for water or mixing.
• We need to find the percentage profit earned on his actual cost.

Concept / Approach:
The key idea is that the cost is only for the milk, not for the water. By adding water, the milkman increases the total selling quantity while the total cost remains the same. Profit percentage is calculated as profit divided by cost price multiplied by 100. So we first compute the total cost of the 20 litres of milk, then compute the total selling price of the 25 litre mixture at Rs. 18 per litre, and finally compute the profit percentage from these values.

Step-by-Step Solution:
Step 1: Cost price of 1 litre of pure milk = Rs. 18.Step 2: Total volume of pure milk = 20 litres.Step 3: Total cost price of milk = 20 * 18 = Rs. 360.Step 4: Volume of water added = 5 litres (water is free, so no cost added).Step 5: Total volume of mixture = 20 + 5 = 25 litres.Step 6: Selling price per litre of mixture = Rs. 18 (same as milk cost price).Step 7: Total selling price of mixture = 25 * 18 = Rs. 450.Step 8: Profit = Selling price minus Cost price = 450 - 360 = Rs. 90.Step 9: Profit percentage = (Profit / Cost price) * 100 = (90 / 360) * 100.Step 10: Simplify the fraction 90 / 360 = 1 / 4.Step 11: Profit percentage = (1 / 4) * 100 = 25%.

Verification / Alternative check:
Another way is to think directly in terms of effective gain in quantity. The milkman paid for 20 litres but sells 25 litres. So the quantity gained over paid quantity is 5 litres on a base of 20 litres. As a fraction that is 5 / 20 = 1 / 4. Multiplying by 100 gives 25% effective gain. This matches the profit percentage computed using cost and selling price, which confirms that the answer is consistent and correct.

Why Other Options Are Wrong:

• 20%: This would be correct if the gained quantity or profit were one fifth of the cost, but here the extra effective quantity is one fourth of the original quantity.
• 33.33%: This would correspond to a gain of one third of the cost price, which does not match the ratio of 5 litres to 20 litres.
• 18%: This is simply close to the cost price per litre (Rs. 18) but has no relation to the actual profit percentage.

Common Pitfalls:

• Students sometimes mistakenly compute profit on 25 litres instead of 20 litres, which leads to wrong logic.
• Another common error is to treat the cost price per litre of the mixture as the same as that of milk without accounting for the added water being free, which hides the profit.
• Some learners confuse absolute profit in rupees with profit percentage, which must always be relative to the cost price.

Final Answer:
The milkman earns a profit of 25% by selling the mixture at the original cost price of pure milk.