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Three vessels having volumes in the ratio of 1 : 3 : 5 are full of a mixture of water and milk. In the first vessel, ratio of water and milk is 7 : 13, in second 9 : 11 and in third 11 : 14. If the liquid in all the three vessels were mixed in a bigger container, what is the resulting ratio of water and milk?
  • a)
    11 : 17
  • b)
    29 : 41
  • c)
    3 : 4
  • d)
    39 : 51
Correct answer is option 'D'. Can you explain this answer?
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Three vessels having volumes in the ratio of 1 : 3 : 5 are full of a m...
Let the three vessels contain 1 litre, 3 litres and 5 litres of water and milk mixture.
In the 1st vessel, 
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Three vessels having volumes in the ratio of 1 : 3 : 5 are full of a m...
Given:
- Volumes of three vessels: 1 : 3 : 5
- Ratio of water and milk in the vessels:
- 1st vessel: 7 : 13
- 2nd vessel: 9 : 11
- 3rd vessel: 11 : 14

To find:
The resulting ratio of water and milk when the liquids from all three vessels are mixed.

Solution:

Step 1: Calculate the total volumes of water and milk in each vessel

- For the 1st vessel:
- Volume of water = (1/20) * Volume of vessel
- Volume of milk = (13/20) * Volume of vessel

- For the 2nd vessel:
- Volume of water = (9/20) * Volume of vessel
- Volume of milk = (11/20) * Volume of vessel

- For the 3rd vessel:
- Volume of water = (11/25) * Volume of vessel
- Volume of milk = (14/25) * Volume of vessel

Step 2: Calculate the total volumes of water and milk when the liquids from all three vessels are mixed.

- Total volume of water = (1/20) * Volume of vessel + (9/20) * Volume of vessel + (11/25) * Volume of vessel
- Total volume of milk = (13/20) * Volume of vessel + (11/20) * Volume of vessel + (14/25) * Volume of vessel

Step 3: Simplify the ratios of water and milk.

- Divide both the total volume of water and total volume of milk by the volume of vessel to get the ratio.

- The resulting ratio of water and milk in the bigger container is the simplified ratio obtained.

- Simplifying the ratio, we get:
- Water : Milk = (11/51) : (40/51)
- Multiplying both sides by 51, we get:
- Water : Milk = 11 : 40

Therefore, the resulting ratio of water and milk when the liquids from all three vessels are mixed is 11 : 40, which is option D.
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Three vessels having volumes in the ratio of 1 : 3 : 5 are full of a mixture of water and milk. In the first vessel, ratio of water andmilk is 7 : 13, in second 9 : 11 and in third 11 : 14. If the liquid in all the three vessels were mixed in a bigger container, what is the resulting ratio of water and milk?a)11 : 17b)29 : 41c)3 : 4d)39 : 51Correct answer is option 'D'. Can you explain this answer?
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