A 6 L mixture contains 75% milk. How many litres of milk must be added to make the mixture 90% milk?

Introduction / Context: We increase the proportion of milk by adding pure milk. This leaves water quantity unchanged while increasing total volume and milk quantity. The target is a 90% milk concentration in the final mixture.

Given Data / Assumptions:

• Initial volume = 6 L; milk = 75% of 6 = 4.5 L; water = 1.5 L.
• Add x L of milk; final volume = 6 + x; final milk = 4.5 + x.
• Target: milk fraction = 0.90.

Concept / Approach: Set up the concentration equation (4.5 + x) / (6 + x) = 0.90 and solve for x. Water remains 1.5 L throughout because only milk is added.

Step-by-Step Solution: (4.5 + x)/(6 + x) = 0.90. 4.5 + x = 0.9(6 + x) = 5.4 + 0.9x. x − 0.9x = 5.4 − 4.5 ⇒ 0.1x = 0.9 ⇒ x = 9 L.

Verification / Alternative check: Final volume = 15 L; milk = 13.5 L; fraction = 13.5/15 = 0.9 = 90%, as required.

Why Other Options Are Wrong: 8, 10, 12 litres do not satisfy the exact 90% equation; only 9 litres works.

Common Pitfalls: Changing water amount by mistake. Only milk is added, so water remains at 1.5 L; adjust only the numerator and denominator accordingly.

Final Answer: 9 liters