Milk with water yielding profit despite lower selling price: Milk costs ₹ 5 per liter. It is mixed with water and sold at ₹ 4 per liter, yet the seller earns a 12.5% profit on outlay. How much water is present per liter of mixture?

Introduction / Context: Even though the selling price is lower than the pure milk cost, profit is possible because water is free. Let the milk fraction in 1 L of mixture be m; the cost per liter is 5*m and revenue is ₹ 4. The profit condition sets a relationship between m and the selling price.

Given Data / Assumptions:

• Cost of milk = ₹ 5/L; water is free.
• Selling price = ₹ 4/L.
• Profit = 12.5% ⇒ revenue = 1.125 * cost.
• Let milk fraction = m ⇒ water fraction = 1 − m.

Concept / Approach: Equation: 4 = 1.125 * (5*m). Solve for m, then compute water fraction (1 − m), which is the liters of water per 1 L of mixture.

Step-by-Step Solution:

Verification / Alternative check: Cost per liter = 5*(32/45) = ₹ 3.555…; 12.5% profit on this is ₹ 0.444…; sum = ₹ 4 exactly.

Why Other Options Are Wrong: 32/45 L is the milk amount, not water; 32/13 L is nonsensical here; 1/4 L does not satisfy the profit equation.

Common Pitfalls: Comparing prices directly without accounting for water’s zero cost; switching milk and water fractions.

Final Answer: 13/45 L