Five litres of water is added to a certain quantity of pure milk costing ₹ 3 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, then what is the amount of pure milk in the mixture? (M.A.T., 2006)

### Concept & Profit from Dilution When a mixture of milk and water is sold at the original cost price of the pure milk, the entire profit percentage is generated directly by the proportion of the "free" addition (water) relative to the paid base (milk). $$Profit\ \% = \left(\frac{Quantity\ of\ Water}{Quantity\ of\ Milk}\right) \times 100$$ ### Step-by-Step Solution * Let the quantity of pure milk be $x$ litres. * Quantity of water added = 5 litres. * The mixture is sold at the same price as the cost price of pure milk. * This means the profit is generated entirely because water costs nothing but is sold at the price of milk. * Therefore, the profit percentage is exactly the ratio of water to milk. * $20\% = \frac{5}{x} \times 100$ * $20 = \frac{500}{x}$ * $x = \frac{500}{20} = 25$ litres. ### Exam Strategy & Shortcut This is a classic and very fast rule: If you sell a milk-water mixture at the CP of milk, the Profit % equals the ratio of Water to Milk. Since 20% is $\frac{1}{5}$, the ratio is Water (1 part) to Milk (5 parts). Since Water (1 part) = 5 litres, Milk (5 parts) = $5 \times 5 = 25$ litres. Solved in 5 seconds without heavy algebra! ### Common Pitfall Attempting to calculate the total cost ($3x$) and total selling price ($3(x+5)$) is mathematically sound but wastes valuable time on an exam compared to using the direct ratio rule. ### Final Answer Therefore, the correct answer is **25 litres**.