In what ratio should water be mixed with milk to gain 16½% (i.e., 16.67%) by selling the mixture at the cost price of milk?

Problem restatementA vendor adds water (free) to milk and sells the mixture at the milk's cost price. What water:milk ratio yields a 16½% profit?

Concept/ApproachAssume 1 litre of milk costs Rs. 1. Add w litres of free water; total litres sold = 1 + w at Rs. 1 per litre.

Step-by-step calculationCost = 1, Revenue = (1 + w) × 1Profit = (1 + w − 1) = w ⇒ Profit% = w × 100%Given 16½% = 1/6 ⇒ w = 1/6Water : Milk = (1/6) : 1 = 1 : 6

Common pitfallsUsing rupee arithmetic instead of the simpler litre-based approach.

Final Answer1 : 6