A 640 ml mixture has milk : water = 6 : 2. How many millilitres of water must be added so that the new mixture becomes half milk and half water?

Introduction / Context: We adjust the composition by adding water only. The milk quantity stays fixed, but total volume and water amount change. The objective is a 50% milk, 50% water mixture after addition.

Given Data / Assumptions:

• Total initial volume = 640 ml.
• Milk : water = 6 : 2 ⇒ milk = 6/8 * 640 = 480 ml; water = 160 ml.
• Add x ml of water; milk remains 480 ml.

Concept / Approach: For a half-and-half mixture, milk volume must equal water volume at the end. Set milk = water_final and solve for x (the added water).

Step-by-Step Solution: Let added water = x ml. Final water = 160 + x; final milk = 480 (unchanged). Set equality: 480 = 160 + x ⇒ x = 320 ml. Therefore, add 320 ml of water.

Verification / Alternative check: New total = 640 + 320 = 960 ml with milk = 480 ml and water = 480 ml, which is exactly 50% each.

Why Other Options Are Wrong: 310, 330, 340 do not equalize milk and water; only 320 matches the requirement.

Common Pitfalls: Trying to proportionally reduce milk, which does not happen here because only water is added. Keep milk constant and balance water to match it.

Final Answer: 320 ml