The ratio of milk to water in a mixture is 5:4. If 2 litres of water is added to the mixture, the ratio becomes 10:9. Find the new amount of water (in litres) in the mixture after adding the 2 litres of water.

Introduction / Context:
This is a ratio update problem where only water is added. Since milk is not removed or added, the milk quantity stays constant. The final ratio is given after the water addition, so you can represent the original mixture using a variable k based on the 5:4 ratio. Then increase only the water part by 2 litres and enforce the final ratio 10:9. Solving the resulting equation gives the original scale and therefore the new water quantity.

Given Data / Assumptions:

• Initial milk:water = 5:4
• Water added = 2 litres
• Final milk:water = 10:9
• Let initial milk = 5k and initial water = 4k

Concept / Approach:
Milk remains 5k. Water becomes 4k + 2 after addition. Apply final ratio: 5k / (4k + 2) = 10/9. Solve for k, then compute the new water amount (4k + 2).

Step-by-Step Solution:
Initial milk = 5k, initial water = 4k After adding 2 litres water: water = 4k + 2 Final ratio 10:9 => 5k/(4k + 2) = 10/9 Cross-multiply: 9*5k = 10*(4k + 2) 45k = 40k + 20 5k = 20 k = 4 New water amount = 4k + 2 = 16 + 2 = 18 litres

Verification / Alternative check:
Milk = 5k = 20 litres. Water new = 18 litres. Ratio 20:18 simplifies to 10:9, exactly matching the condition, so the computed new water amount is correct.

Why Other Options Are Wrong:
16 litres would imply ratio 20:16 = 5:4, meaning no effective change after addition. 12, 14, 17 do not yield 10:9 when milk remains fixed and only water increases by 2.

Common Pitfalls:
Adding 2 litres to milk by mistake, setting up the equation as (milk + 2)/water, or simplifying ratios incorrectly after solving for k.

Final Answer:
The new amount of water in the mixture is 18 litres.