A man buys milk at ? 4 per litre, mixes it with water and...

A man buys milk at $? 4$ per litre, mixes it with water and sells the mixture at the same price. If his profit is $25 \%$, find the amount of water mixed with each litre of milk.
(A) $0.25$ litres
(B) $0.5$ litres
(C) $0.75$ litres
(D) $0.6$ litres

Key Concepts

Cost Price Analysis in Adulteration

Cost price analysis in the context of adulteration examines how the addition of an inexpensive or free component affects the overall cost of a product. When a product is mixed with a cost-free substance, the real cost per unit of the mixture decreases, which results in a profit even if the mixture is sold at the original price of the pure product. This concept is crucial when evaluating problems that combine elements of mixture and profit calculation.

Profit Percentage

Profit percentage is a measure of the gain or profit made compared to the cost price, expressed as a percentage. It is calculated by dividing the profit by the cost price and multiplying by 100. In scenarios where ingredients are diluted or adulterated, understanding profit percentage helps in assessing how the addition of a cost-free component can enhance profitability when the selling price remains unchanged.

Dilution in Mixture Problems

Dilution in mixture problems involves adding a substance that does not cost or has negligible cost, such as water, to a product like milk. This lowers the average cost of the final mixture while the selling price per unit remains the same, leading to an increase in profit margin. It is a common method in mixture problems to demonstrate how adding a cheaper component can affect the overall cost and profit calculation.

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