Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is?

Given: Three mixtures of equal quantity are taken, with the following Milk : Water ratios:

• Mixture 1 → 1 : 2
• Mixture 2 → 2 : 3
• Mixture 3 → 3 : 4

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.