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Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.
- a)2 : 1, 3 : 4
- b)1 : 3, 1 : 2
- c)2 : 3, 4 : 1
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two equal containers are filled with a mixture of water and alcohol. O...
To solve this problem, let's assume that the capacity of each container is 'x' liters.
Let's calculate the amount of alcohol and water in each container separately.
Let the amount of alcohol in the first container be 'a' liters.
Therefore, the amount of water in the first container will be (x - a) liters.
According to the given information, the second container contains three times as much alcohol as the first container.
So, the amount of alcohol in the second container will be 3a liters.
Therefore, the amount of water in the second container will be (x - 3a) liters.
Now, let's calculate the total amount of alcohol and water in both containers when they are mixed.
When the mixtures in the two containers are mixed, the total amount of alcohol will be (a + 3a) = 4a liters.
Similarly, the total amount of water will be ((x - a) + (x - 3a)) = 2x - 4a liters.
It is given that the ratio of water to alcohol in the mixture is 3:2.
So, we can write the equation:
(2x - 4a)/(4a) = 3/2
Cross-multiplying, we get:
4(2x - 4a) = 3(4a)
8x - 16a = 12a
8x = 28a
2x = 7a
Now, let's calculate the ratio of water to alcohol in each of the original containers.
In the first container:
Water = x - a
Alcohol = a
Ratio = (x - a)/a = x/a - 1
In the second container:
Water = x - 3a
Alcohol = 3a
Ratio = (x - 3a)/(3a) = x/(3a) - 1/3
From the equation 2x = 7a, we can write x/a = 7/2.
So, the ratio of water to alcohol in the first container is:
x/a - 1 = 7/2 - 1 = 5/2
And the ratio of water to alcohol in the second container is:
x/(3a) - 1/3 = 7/(3*2) - 1/3 = 7/6 - 1/3 = 4/6 = 2/3
Therefore, the ratio of water to alcohol in each of the original containers is 5:2 and 2:3, which corresponds to option C.
Let's calculate the amount of alcohol and water in each container separately.
Let the amount of alcohol in the first container be 'a' liters.
Therefore, the amount of water in the first container will be (x - a) liters.
According to the given information, the second container contains three times as much alcohol as the first container.
So, the amount of alcohol in the second container will be 3a liters.
Therefore, the amount of water in the second container will be (x - 3a) liters.
Now, let's calculate the total amount of alcohol and water in both containers when they are mixed.
When the mixtures in the two containers are mixed, the total amount of alcohol will be (a + 3a) = 4a liters.
Similarly, the total amount of water will be ((x - a) + (x - 3a)) = 2x - 4a liters.
It is given that the ratio of water to alcohol in the mixture is 3:2.
So, we can write the equation:
(2x - 4a)/(4a) = 3/2
Cross-multiplying, we get:
4(2x - 4a) = 3(4a)
8x - 16a = 12a
8x = 28a
2x = 7a
Now, let's calculate the ratio of water to alcohol in each of the original containers.
In the first container:
Water = x - a
Alcohol = a
Ratio = (x - a)/a = x/a - 1
In the second container:
Water = x - 3a
Alcohol = 3a
Ratio = (x - 3a)/(3a) = x/(3a) - 1/3
From the equation 2x = 7a, we can write x/a = 7/2.
So, the ratio of water to alcohol in the first container is:
x/a - 1 = 7/2 - 1 = 5/2
And the ratio of water to alcohol in the second container is:
x/(3a) - 1/3 = 7/(3*2) - 1/3 = 7/6 - 1/3 = 4/6 = 2/3
Therefore, the ratio of water to alcohol in each of the original containers is 5:2 and 2:3, which corresponds to option C.
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Community Answer
Two equal containers are filled with a mixture of water and alcohol. O...
Step 1: Let the amount of alcohol in container A be x. Then, the amount of alcohol in container B is 3x (since container B contains three times as much alcohol as container A).Step 2: When the contents of containers A and B are mixed, the total amount of water in both containers is 3 parts (from the 3:2 water to alcohol ratio), and the total amount of alcohol is 2 parts.Step 3: Since the mixture from containers A and B were mixed together, the ratio of water to alcohol in each container would be the same. Let's find this ratio.In container A:Amount of water = 3 parts - x (since the total is 3 parts and x parts are alcohol).Amount of alcohol = x parts.In container B:Amount of water = 3 parts - 3x (since the total is 3 parts and 3x parts are alcohol).Amount of alcohol = 3x parts.Step 4: Now, we equate the ratio of water to alcohol in both containers:For container A:Water : Alcohol = (3 - x) : xFor container B:Water : Alcohol = (3 - 3x) : 3xStep 5: Since the ratio is the same, we can set them equal to each other and solve for x:(3 - x) : x = (3 - 3x) : 3xStep 6: Cross-multiply and solve for x:3(3x) = x(3 - x)9x = 3x - x^2x^2 - 6x = 0x(x - 6) = 0Step 7: We have two possible solutions for x: x = 0 or x = 6.However, x cannot be 0 because container A needs to contain alcohol. So, we choose x = 6.Step 8: Now that we have x = 6, we can find the amount of alcohol in each container:In container A:Amount of alcohol = x = 6 partsIn container B:Amount of alcohol = 3x = 3 * 6 = 18 partsStep 9: Finally, we express the ratio of alcohol in each container:Container A : Container B = 6 : 18 = 2 : 6 = 1 : 3So, the correct option is C) 2:3, 4:1.
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Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.a)2 : 1, 3 : 4b)1 : 3, 1 : 2c)2 : 3, 4 : 1d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.a)2 : 1, 3 : 4b)1 : 3, 1 : 2c)2 : 3, 4 : 1d)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.a)2 : 1, 3 : 4b)1 : 3, 1 : 2c)2 : 3, 4 : 1d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.a)2 : 1, 3 : 4b)1 : 3, 1 : 2c)2 : 3, 4 : 1d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.a)2 : 1, 3 : 4b)1 : 3, 1 : 2c)2 : 3, 4 : 1d)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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