Three bottles of equal capacity contain milk-water mixtures in the ratios 2:5, 3:4, and 4:5 respectively (milk:water). All three bottles are emptied into a large container. What will be the ratio of milk to water in the final mixture in the large container?

Introduction / Context:
This question tests combining mixtures with equal volumes. Because all three bottles have equal capacity, you can assume each bottle contains 1 litre (or any same unit volume). Then compute the milk fraction and water fraction for each bottle based on its ratio. Add total milk from all bottles and add total water from all bottles. Finally, express the totals as a simplified ratio. The most common mistake is trying to add ratios directly, which is not valid.

Given Data / Assumptions:

• Bottle 1 milk:water = 2:5
• Bottle 2 milk:water = 3:4
• Bottle 3 milk:water = 4:5
• All bottles have equal capacity
• Assume each bottle has 1 litre for calculation

Concept / Approach:
For ratio a:b, milk fraction = a/(a+b) and water fraction = b/(a+b). Compute fractions for each bottle, sum milk and sum water. Convert to integer ratio by using a common denominator and then simplify if possible.

Step-by-Step Solution:
Bottle 1 (2:5): milk = 2/7, water = 5/7 Bottle 2 (3:4): milk = 3/7, water = 4/7 Bottle 3 (4:5): milk = 4/9, water = 5/9 Total milk = 2/7 + 3/7 + 4/9 = 5/7 + 4/9 Use denominator 63: 5/7 = 45/63 and 4/9 = 28/63 Total milk = (45 + 28)/63 = 73/63 Total water = 5/7 + 4/7 + 5/9 = 9/7 + 5/9 Convert to /63: 9/7 = 81/63 and 5/9 = 35/63 Total water = (81 + 35)/63 = 116/63 Final ratio milk:water = (73/63):(116/63) = 73:116

Verification / Alternative check:
Since the denominator 63 cancels out, only the numerators matter. Also, 73 is prime relative to 116 (no common factor), so the ratio is already in simplest form.

Why Other Options Are Wrong:
73:113 and 73:106 come from incorrect water totals or wrong fraction conversion for 4:5. 73:189 is far too water-heavy and indicates a major arithmetic error. 59:94 does not match the exact computed totals.

Common Pitfalls:
Adding ratios directly (2+3+4):(5+4+5), forgetting equal capacity assumption, or using 4/5 instead of 4/9 for the third bottle milk fraction.

Final Answer:
The final ratio of milk to water is 73:116.