A milk-water mixture contains milk equal to 2/3 of the mixture. The total mixture available is 21 litres.\nIf 4 litres of water is added to this mixture, what will be the new percentage of milk in the resulting mixture?

Introduction:
This problem checks fraction-to-percentage conversion in mixtures. When water is added, the amount of milk remains unchanged, but the total volume increases. The milk percentage therefore decreases. We compute milk litres first, then divide by the new total and convert to percent.

Given Data / Assumptions:

• Total mixture initially = 21 litres
• Milk fraction initially = 2/3 of mixture
• Water added = 4 litres
• Milk amount stays constant

Concept / Approach:
Milk amount = (2/3) * 21. New total = 21 + 4. New milk percentage = (milk / new total) * 100.

Step-by-Step Solution:
Initial milk = (2/3) * 21 = 14 litresInitial water = 21 - 14 = 7 litresAfter adding 4 litres water, water becomes = 7 + 4 = 11 litresNew total mixture = 21 + 4 = 25 litresMilk remains = 14 litresNew milk percentage = (14 / 25) * 100 = 56%

Verification / Alternative Check:
Since milk is 14 litres out of 25 litres total, the fraction is 14/25. Converting to percent: 14 * 4 = 56, so 56%. This confirms the computed value without long division.

Why Other Options Are Wrong:
44%: would mean milk is 11 litres, but milk did not decrease.50%: would mean milk equals water, but milk is still more than water.60% or 40%: inconsistent with 14 litres milk out of 25 litres total.

Common Pitfalls:
Assuming milk amount changes when only water is added.Computing 2/3 of (21+4) instead of 2/3 of 21.Forgetting to convert fraction to percentage correctly.

Final Answer:
56%