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There are three vessels each of 20 litre capacity is filled with the mixture of milk and water. The ratio of milk and water are 2:3, 3:4 and 4:5 respectively. All the vessels are emptied into fourth vessel, then find the ratio of milk and water in the final mixture.
- a)401/543
- b)401/544
- c)401/545
- d)401/546
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are three vessels each of 20 litre capacity is filled with the m...
Answer – b) 401/544 Explanation : Milk = 2/5 + 3/7 + 4/9 and water = 3/5 + 4/7 + 5/9 so ratio will be 401/544
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There are three vessels each of 20 litre capacity is filled with the m...
Solution:
Given:
- There are three vessels, each with a capacity of 20 liters.
- The ratio of milk and water in the first vessel is 2:3.
- The ratio of milk and water in the second vessel is 3:4.
- The ratio of milk and water in the third vessel is 4:5.
To find:
- The ratio of milk and water in the final mixture when all three vessels are emptied into a fourth vessel.
Let's calculate the quantity of milk and water in each vessel:
- In the first vessel, the quantity of milk = (2/5) * 20 = 8 liters and the quantity of water = (3/5) * 20 = 12 liters.
- In the second vessel, the quantity of milk = (3/7) * 20 = 8.57 liters (approx) and the quantity of water = (4/7) * 20 = 11.43 liters (approx).
- In the third vessel, the quantity of milk = (4/9) * 20 = 8.89 liters (approx) and the quantity of water = (5/9) * 20 = 11.11 liters (approx).
Now, let's calculate the total quantity of milk and water in the final mixture:
- The total quantity of milk = 8 + 8.57 + 8.89 = 25.46 liters (approx).
- The total quantity of water = 12 + 11.43 + 11.11 = 34.54 liters (approx).
Therefore, the ratio of milk and water in the final mixture is approximately 25.46:34.54, which can be simplified to 401:544.
Hence, the correct answer is option B) 401/544.
Given:
- There are three vessels, each with a capacity of 20 liters.
- The ratio of milk and water in the first vessel is 2:3.
- The ratio of milk and water in the second vessel is 3:4.
- The ratio of milk and water in the third vessel is 4:5.
To find:
- The ratio of milk and water in the final mixture when all three vessels are emptied into a fourth vessel.
Let's calculate the quantity of milk and water in each vessel:
- In the first vessel, the quantity of milk = (2/5) * 20 = 8 liters and the quantity of water = (3/5) * 20 = 12 liters.
- In the second vessel, the quantity of milk = (3/7) * 20 = 8.57 liters (approx) and the quantity of water = (4/7) * 20 = 11.43 liters (approx).
- In the third vessel, the quantity of milk = (4/9) * 20 = 8.89 liters (approx) and the quantity of water = (5/9) * 20 = 11.11 liters (approx).
Now, let's calculate the total quantity of milk and water in the final mixture:
- The total quantity of milk = 8 + 8.57 + 8.89 = 25.46 liters (approx).
- The total quantity of water = 12 + 11.43 + 11.11 = 34.54 liters (approx).
Therefore, the ratio of milk and water in the final mixture is approximately 25.46:34.54, which can be simplified to 401:544.
Hence, the correct answer is option B) 401/544.
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