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Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
- a)99:61
- b)99:160
- c)61:160
- d)61:99
- e)99:16
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two vessels having volumes in the ratio 3:5 are filled with water and ...
Let the volumes of the two vessels be 3x and 5x, where x is a common factor.
The first vessel contains a milk and water solution in the ratio 2:3.
This means that for every 2 units of milk, there are 3 units of water.
Therefore, the first vessel contains (2/5) * 3x = (6/5)x units of milk and (3/5) * 3x = (9/5)x units of water.
The first vessel contains a milk and water solution in the ratio 2:3.
This means that for every 2 units of milk, there are 3 units of water.
Therefore, the first vessel contains (2/5) * 3x = (6/5)x units of milk and (3/5) * 3x = (9/5)x units of water.
Similarly, the second vessel contains a milk and water solution in the ratio 3:1.
This means that for every 3 units of milk, there is 1 unit of water.
So, the second vessel contains (3/4) * 5x = (15/4)x units of milk and (1/4) * 5x = (5/4)x units of water.
This means that for every 3 units of milk, there is 1 unit of water.
So, the second vessel contains (3/4) * 5x = (15/4)x units of milk and (1/4) * 5x = (5/4)x units of water.
Now, when we combine the contents of both vessels into a larger vessel, we add up the amounts of milk and water from each vessel.
The total amount of milk in the larger vessel is (6/5)x + (15/4)x = (48x + 75x)/(20) = (123x)/(20).
Similarly, the total amount of water in the larger vessel is (9/5)x + (5/4)x = (36x + 25x)/(20) = (61x)/(20).
The total amount of milk in the larger vessel is (6/5)x + (15/4)x = (48x + 75x)/(20) = (123x)/(20).
Similarly, the total amount of water in the larger vessel is (9/5)x + (5/4)x = (36x + 25x)/(20) = (61x)/(20).
Therefore, the ratio of milk to water in the larger vessel is (123x)/(20) : (61x)/(20).
To simplify this ratio, we can divide both terms by x, as x is a common factor:
To simplify this ratio, we can divide both terms by x, as x is a common factor:
Ratio = 123 : 61
This means that the ratio of milk to water in the larger vessel is 123:61.
Comparing this with the answer choices provided, we can see that the correct answer is indeed A) 99:61.
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Community Answer
Two vessels having volumes in the ratio 3:5 are filled with water and ...
Given:
- The volumes of the two vessels are in the ratio 3:5.
- The ratio of milk to water in the first vessel is 2:3.
- The ratio of milk to water in the second vessel is 3:1.
To find:
- The ratio of milk to water in the larger vessel.
Solution:
Let's assume that the volumes of the two vessels are 3x and 5x respectively.
The first vessel contains a mixture of milk and water in the ratio 2:3. So, the quantity of milk in the first vessel is (2/5) * 3x = (6/5)x, and the quantity of water is (3/5) * 3x = (9/5)x.
The second vessel contains a mixture of milk and water in the ratio 3:1. So, the quantity of milk in the second vessel is (3/4) * 5x = (15/4)x, and the quantity of water is (1/4) * 5x = (5/4)x.
When the contents of both vessels are emptied into a larger vessel, the total quantity of milk in the larger vessel will be (6/5)x + (15/4)x = (24/20)x + (75/20)x = (99/20)x.
Similarly, the total quantity of water in the larger vessel will be (9/5)x + (5/4)x = (36/20)x + (25/20)x = (61/20)x.
Therefore, the ratio of milk to water in the larger vessel is (99/20)x : (61/20)x, which simplifies to 99:61.
Hence, the correct answer is option A) 99:61.
- The volumes of the two vessels are in the ratio 3:5.
- The ratio of milk to water in the first vessel is 2:3.
- The ratio of milk to water in the second vessel is 3:1.
To find:
- The ratio of milk to water in the larger vessel.
Solution:
Let's assume that the volumes of the two vessels are 3x and 5x respectively.
The first vessel contains a mixture of milk and water in the ratio 2:3. So, the quantity of milk in the first vessel is (2/5) * 3x = (6/5)x, and the quantity of water is (3/5) * 3x = (9/5)x.
The second vessel contains a mixture of milk and water in the ratio 3:1. So, the quantity of milk in the second vessel is (3/4) * 5x = (15/4)x, and the quantity of water is (1/4) * 5x = (5/4)x.
When the contents of both vessels are emptied into a larger vessel, the total quantity of milk in the larger vessel will be (6/5)x + (15/4)x = (24/20)x + (75/20)x = (99/20)x.
Similarly, the total quantity of water in the larger vessel will be (9/5)x + (5/4)x = (36/20)x + (25/20)x = (61/20)x.
Therefore, the ratio of milk to water in the larger vessel is (99/20)x : (61/20)x, which simplifies to 99:61.
Hence, the correct answer is option A) 99:61.
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Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.a)99:61b)99:160c)61:160d)61:99e)99:16Correct answer is option 'A'. Can you explain this answer?
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