A 640 ml milk-water mixture has milk and water in the ratio 6 : 2. Water is added to this mixture.\nHow much water (in ml) must be added so that the new mixture becomes exactly half milk and half water (i.e., milk : water becomes 1 : 1)?

Introduction:
This question checks ratio-based mixture adjustment. When only water is added, the amount of milk remains constant while total volume increases, reducing the milk percentage. To make the final mixture half milk and half water, we set milk amount equal to water amount (or milk percentage to 50%).

Given Data / Assumptions:

• Total mixture = 640 ml
• Milk : Water = 6 : 2
• Only water is added (milk amount stays the same)
• Final requirement: milk and water equal (50% milk)

Concept / Approach:
Find the initial milk quantity using ratio parts. Then add x ml water so that milk becomes half of the total mixture:\nMilk = (Total + x) / 2.

Step-by-Step Solution:
Total parts = 6 + 2 = 8Milk amount = (6/8) * 640 = 480 mlWater amount = (2/8) * 640 = 160 mlLet added water = x mlNew total volume = 640 + xFor half milk: 480 = (640 + x) / 2960 = 640 + xx = 320 ml

Verification / Alternative Check:
After adding 320 ml water:\nMilk = 480 ml, Water = 160 + 320 = 480 ml. So milk : water = 480 : 480 = 1 : 1 and milk percentage = 50%, exactly satisfying the requirement.

Why Other Options Are Wrong:
310 ml or 330 ml: would not make milk and water exactly equal.360 ml or 400 ml: adds too much water, making milk percentage less than 50%.

Common Pitfalls:
Treating 6:2 as 6%:2% instead of a ratio.Changing milk amount even though only water is added.Forgetting to convert the ratio into actual quantities using total parts.

Final Answer:
320 ml