An 80 litre mixture of milk and water contains 10% milk. How many litres of milk must be added to this mixture so that the water percentage becomes 80% in the new mixture?

Introduction:This question tests percentage composition changes when only milk is added. Adding milk increases total volume and increases milk amount, while water amount stays constant. To make water percentage 80%, the milk percentage must become 20%. We use a simple equation using constant water quantity.

Given Data / Assumptions:

• Total mixture initially = 80 litres
• Milk percentage initially = 10%
• So water percentage initially = 90%
• Only milk is added
• Target water percentage = 80%

Concept / Approach:Find initial water amount (constant). Let x litres milk be added. Then new total = 80 + x. Target condition:water / (80 + x) = 0.80.

Step-by-Step Solution:Initial milk = 10% of 80 = 8 litresInitial water = 80 - 8 = 72 litresLet added milk = x litresNew total = 80 + xWater remains = 72 litresTarget: 72 / (80 + x) = 0.8072 = 0.80(80 + x) = 64 + 0.80x8 = 0.80xx = 10 litres

Verification / Alternative Check:After adding 10 litres milk:Total = 90 litres. Water = 72 litres.Water% = 72/90 = 0.80 = 80%, correct. Milk becomes 18 litres, which is 20% of 90 litres, consistent with the target split.

Why Other Options Are Wrong:8 or 9 litres: total too small, so water% stays above 80%.12 or 16 litres: adds too much milk, making water% fall below 80%.

Common Pitfalls:Assuming water changes when only milk is added.Using 80% of original 80 litres instead of 80% of (80 + x).Forgetting that water% target implies milk% target automatically.

Final Answer:10 litres