Correct Answer: 193 : 122
Explanation:
Given: Three mixtures of equal quantity are taken, with the following Milk : Water ratios:
Step 1: Assume quantity of each mixture is 1 litre.
That means we have 1 litre of each mixture with given milk and water ratios.
Mixture 1: 1 : 2
Total parts = 1 + 2 = 3
Milk = 1/3 litre
Water = 2/3 litre
Mixture 2: 2 : 3
Total parts = 2 + 3 = 5
Milk = 2/5 litre
Water = 3/5 litre
Mixture 3: 3 : 4
Total parts = 3 + 4 = 7
Milk = 3/7 litre
Water = 4/7 litre
Step 2: Add all milk and water from the three mixtures
Milk = (1/3 + 2/5 + 3/7) litres
Water = (2/3 + 3/5 + 4/7) litres
Step 3: Calculate LCM to add fractions
Milk:
LCM of 3, 5, 7 = 105
= (35 + 42 + 45) / 105 = 122 / 105 litres
Water:
= (70 + 63 + 60) / 105 = 193 / 105 litres
Step 4: Final Ratio = Water : Milk = 193 : 122
Answer: 193 : 122
This ratio is already in its lowest form. So, when equal quantities of three mixtures in ratios 1:2, 2:3, and 3:4 are mixed, the final water-to-milk ratio is 193:122.
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