A milkman claims to sell at cost price but mixes water and gains 25%. What percentage of the mixture is water?

Problem restatementA vendor sells a milk–water mixture at the cost price of pure milk and still makes a 25% profit. Determine the percentage of water in the mixture.

Given data

• Selling price per litre (SP) equals the cost price of pure milk per litre (assume Rs. 1 for convenience).
• Profit = 25%.

Concept/ApproachIf SP = 1 and profit is 25%, then the effective cost price of the mixture must be 1 ÷ 1.25 = 0.8. Since only milk has cost and water is free, the fraction of milk in the mixture must equal 0.8. Hence water fraction = 1 − 0.8 = 0.2 = 20%.

Step-by-step calculationSP = 1 (assumption)Profit% = 25% ⇒ Mixture CP = 1 ÷ 1.25 = 0.8Milk fraction = 0.8 ⇒ Water fraction = 1 − 0.8 = 0.2 = 20%

Common pitfallsUsing absolute rupee values unnecessarily or forgetting that water costs zero, so only the milk fraction contributes to cost.

Final Answer20%