Alligation–Mixture (Milk–Water):\nA mixture has milk:water = 5:4. After adding 2 litres of water, the ratio becomes 10:9. Find the new amount of water (in litres) in the mixture.

Introduction / Context:
Classic mixture problems require ratio translation into actual quantities and careful updates after additions.

Given Data / Assumptions:

• Initial milk:water = 5:4.
• Add 2 L water; new ratio = 10:9.
• Volumes add linearly; no evaporation/spillage.

Concept / Approach:
Let initial milk = 5k and water = 4k. After adding 2 L water, milk stays 5k; water becomes 4k + 2. New ratio condition gives an equation to solve for k.

Step-by-Step Solution:
1) 5k / (4k + 2) = 10 / 92) Cross-multiply: 45k = 40k + 20 ⇒ 5k = 20 ⇒ k = 4.3) New water = 4k + 2 = 16 + 2 = 18 L.

Verification / Alternative check:
Milk = 5k = 20 L; water = 18 L ⇒ ratio 20:18 = 10:9 (checks).

Why Other Options Are Wrong:
16 L ignores the added 2 L; 20 L overshoots; 14 L is inconsistent with the target ratio.

Common Pitfalls:
Changing milk quantity (it doesn’t change here); mixing up which component was added.

Final Answer:
18 litres