Profit by adulteration (water to milk): A milk seller pays ₹ 500 per kiloliter (i.e., ₹ 0.50 per liter) for pure milk. He adds water and sells the mixture at ₹ 0.56 per liter, making an overall profit of 40%. What is the ratio of water to milk supplied to customers?

Introduction / Context: Since water is free, the cost of 1 L of mixture equals the cost of the milk fraction alone. The given selling price and profit percentage let us compute the cost per liter of mixture; from that we deduce the milk fraction and hence the water:milk ratio.

Given Data / Assumptions:

• Milk cost = ₹ 0.50 per L.
• Selling price = ₹ 0.56 per L.
• Profit = 40% ⇒ SP = 1.4 * cost_per_liter_of_mixture.

Concept / Approach: cost_per_liter_mixture = 0.56 / 1.4 = ₹ 0.40. If milk fraction is m, then cost_per_liter_mixture = 0.50 * m (water is free). Solve for m, then water fraction = 1 − m, and ratio water:milk follows.

Step-by-Step Solution:

Verification / Alternative check: Check profit: cost 0.40 ⇒ profit 40% ⇒ 0.16 ⇒ SP = 0.56, matching the statement.

Why Other Options Are Wrong: Other ratios correspond to milk fractions different from 0.80 and would not satisfy the 40% profit at ₹ 0.56/L.

Common Pitfalls: Treating ₹ 500 per kiloliter incorrectly (it is ₹ 0.50 per liter); forgetting water’s zero cost.

Final Answer: 1 : 4