Milk and water are mixed in vessel A in the ratio 4:1 (milk:water). Milk and water are mixed in vessel B in the ratio 3:2 (milk:water). If equal quantities are taken from vessel A and vessel B and poured into vessel C, what will be the final ratio of milk to water in vessel C?

Introduction / Context:
This problem checks your ability to combine mixtures by using fractions. When equal amounts are taken from two vessels, you can assume 1 unit from each vessel. Then compute milk and water amounts using the given ratios, add them, and form the final ratio.

Given Data / Assumptions:

• Vessel A ratio milk:water = 4:1
• Vessel B ratio milk:water = 3:2
• Equal quantities are taken from A and B
• Assume 1 litre from A and 1 litre from B (any equal volume works)

Concept / Approach:
Convert each ratio into fractions of milk and water. Then add milk amounts and add water amounts to get the combined ratio.

Step-by-Step Solution:

Verification / Alternative check:
You can also do it by taking 5 litres from each vessel. From A: milk 4, water 1. From B: milk 3, water 2. Combined: milk 7, water 3, giving 7:3 again.

Why Other Options Are Wrong:

Common Pitfalls:
A frequent mistake is mixing ratios directly (like adding 4:1 and 3:2) without converting to fractions and using equal quantities. Another mistake is forgetting that equal quantities mean equal total volumes, not equal milk volumes.

Final Answer:
7:3