A 40-litre mixture of milk and water contains 10% water. How many litres of water should be added so that water becomes 20% of the new mixture?

Introduction / Context:
Mixture percentage problems rely on conserving the amount of each component while adjusting total volume. Initially, the amount of water is known from the given percentage. Adding pure water increases both the water amount and the total volume; set up an equation for the target percentage.

Given Data / Assumptions:

• Total initial volume = 40 L.
• Initial water = 10% of 40 L = 4 L (so milk = 36 L).
• Let added water be w L; no milk is added or removed.
• Target: water to be 20% of final mixture.

Concept / Approach:
Final water amount = 4 + w. Final total volume = 40 + w. Target ratio: (4 + w)/(40 + w) = 0.20. Solve for w.

Step-by-Step Solution:

Verification / Alternative check:
New mixture = 45 L with water 9 L? Wait, check: 4 + 5 = 9; 9/45 = 1/5 = 20%. Correct.

Why Other Options Are Wrong:
4 L gives 8/44 ≈ 18.18%; 6.5 L or 7.5 L overshoot 20%.

Common Pitfalls:
Using milk volume as the base or forgetting that added water increases the denominator as well as the numerator.

Final Answer:
5 litres