Explanation:

Correct option 2: 3691 : 4499

To determine the combined ratio of water to milk when mixing the contents of three vessels with given ratios, follow these steps:

Given Ratios:

• Vessel 1: Water : Milk = 6 : 7
• Vessel 2: Water : Milk = 5 : 9
• Vessel 3: Water : Milk = 8 : 7

Calculate Total Parts in Each Vessel

Each ratio represents parts of water and milk. Sum these to find total parts per vessel:

• Vessel 1: 6 (water) + 7 (milk) = 13 parts
• Vessel 2: 5 (water) + 9 (milk) = 14 parts
• Vessel 3: 8 (water) + 7 (milk) = 15 parts

Now, Lets determine Proportions of Water and Milk

Assuming equal volumes from each vessel are mixed, calculate the proportion of water and milk contributed by each:

Water Contribution

Vessel 1 =  6/13

Vessel 2 =  5/14

Vessel 3 =  8/15

Milk Contribution

Vessel 1 =  7/13

Vessel 2 =  9/14

Vessel 3 =  7/15

Normalize to a Common Denominator

To combine these fractions, find the least common denominator (LCD). The denominators are 13, 14, and 15. The LCD is 2730.

Convert Fractions and Sum Contributions

Convert each fraction to have the denominator 2730, then sum:

Water Total:

Vessel 1 :  6/13:1260/2730

Vessel 2 : 5/14: 975/2730

Vessel 3 : 8/15: 1456/2730

Total Water = ( 1470+1755+1274) / 2730= 4499/2730

Determine the Final Ratio

The combined ratio of water to milk is:

Water:Milk=3691:4499