A mixture initially has milk and water in the ratio 5 : 1. After adding 5 litres of water, the ratio becomes 5 : 2. What is the quantity of milk in the original mixture?

Introduction / Context: We are given a mixture ratio that changes after adding a known quantity of water. Since milk remains constant, we solve for the initial amounts consistent with both ratios.

Given Data / Assumptions:

• Initial ratio milk : water = 5 : 1 ⇒ milk = 5x, water = x.
• After adding 5 L of water: milk : water = 5 : 2.
• Find milk quantity 5x.

Concept / Approach: Use the relationship 5x : (x + 5) = 5 : 2. Solve for x, then compute milk = 5x.

Step-by-Step Solution: (5x) / (x + 5) = 5 / 2. Cross-multiply: 10x = 5x + 25. 5x = 25 ⇒ x = 5. Milk = 5x = 25 litres.

Verification / Alternative check: Initial water = x = 5 L; after adding 5 L, water becomes 10 L. Ratio milk : water = 25 : 10 = 5 : 2, as required.

Why Other Options Are Wrong: 16, 32.5, or 22.75 litres do not satisfy the changed ratio when 5 L water is added.

Common Pitfalls: Adding 5 L to both milk and water (incorrect) or misreading which component changes. Only water increases; milk stays the same.

Final Answer: 25 litres