In a mixture of 60 litres, the ratio of milk to water is 2:1. How many litres of water must be added to the mixture so that the new ratio of milk to water becomes 1:2?

Introduction / Context:
This is a ratio-change problem where only water is added. The most important idea is that milk stays constant because nothing is removed and only water is poured in. So you first convert the initial ratio and total volume into actual milk and water quantities. Then you add x litres of water and impose the target ratio. This involves a simple equation but requires careful handling of the ratio meaning.

Given Data / Assumptions:

• Total mixture = 60 litres
• Initial milk:water = 2:1
• Only water is added
• Target milk:water = 1:2
• Let added water = x litres

Concept / Approach:
From 2:1, total parts are 3. Milk = (2/3)*60 and water = (1/3)*60. After adding x, milk stays the same and water becomes (20 + x). For target 1:2, milk/water must equal 1/2.

Step-by-Step Solution:
Total parts = 2 + 1 = 3 Milk = (2/3) * 60 = 40 litres Water = (1/3) * 60 = 20 litres After adding x: water = 20 + x Target ratio 1:2 => 40 / (20 + x) = 1/2 Cross-multiply: 80 = 20 + x x = 60 litres

Verification / Alternative check:
After adding 60 litres, water becomes 80 litres while milk remains 40 litres. Ratio is 40:80 which simplifies to 1:2, exactly as required. This also makes sense because you need water to become double the milk quantity.

Why Other Options Are Wrong:
42 and 56 do not make water reach 80 litres, so the ratio will not become 1:2. 77 makes water too large, producing a ratio smaller than 1:2. 50 makes water 70, giving ratio 40:70 = 4:7, not 1:2.

Common Pitfalls:
Changing milk when only water is added, using total volume after addition incorrectly, or flipping the target ratio as 2:1 instead of 1:2.

Final Answer:
60 litres of water must be added.