A milkman has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when he sells all the mixture at cost price, the profit %?

Step 1: Understand the initial setup

• The milkman has 20 liters of pure milk.
• He adds 5 liters of water, which is free (no cost).
• Total quantity of mixture = 20 + 5 = 25 liters.
• He sells the mixture at Rs. 18 per litre — the cost price of milk.

Step 2: Calculate the cost price of the entire milk

Cost of 20 liters of pure milk = 20 × 18 = Rs. 360

Step 3: Calculate the selling price of the mixture

Selling price = 25 liters × Rs. 18 = Rs. 450

Step 4: Calculate the profit

Profit = Selling Price - Cost Price = Rs. 450 - Rs. 360 = Rs. 90

Step 5: Calculate the profit percentage

Profit % = (Profit / Cost Price) × 100
          = (90 / 360) × 100
          = 25%

Answer: 25%

The milkman gains a profit of 25% by mixing 5 liters of free water into 20 liters of milk and selling the entire 25 liters at the original cost price.

This problem demonstrates a classic example of adulteration where water is mixed into milk to increase quantity without increasing cost. It’s widely used in aptitude exams and real-life business scenarios. The concept teaches how profit can be made without increasing selling price, simply by adding a free ingredient like water.

It’s an excellent question for students preparing for competitive exams, interviews, or improving their quantitative aptitude.