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Solution A is made up of alcohol and water mixed in the ratio of 21:4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2:3 by volume. If Solution A and Solution B are mixed in the ratio of 5:6 by volume, what percent of the resultant mixture is alcohol?
- a)32.5%
- b)40%
- c)60%
- d)65%
- e)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Solution A is made up of alcohol and water mixed in the ratio of 21:4 ...
Given:
To Find: % of alcohol in Resultant Solution
Approach:
- where CA = volume of alcohol in Solution A per unit volume of Solution A and CB = volume of alcohol in Solution B per unit volume of Solution B
We already know the ratio of 
And using our inferences in the Given section, we can easily find the values of CB and CB and thus, answer the question.
And using our inferences in the Given section, we can easily find the values of CB and CB and thus, answer the question.Working out:
- Getting to the required answer
- % of alcohol in Resultant Solution
- % of alcohol in Resultant Solution
Looking at the answer choices, we see that the correct answer is Option C
Most Upvoted Answer
Solution A is made up of alcohol and water mixed in the ratio of 21:4 ...
To solve this problem, we need to find the percentage of alcohol in the resultant mixture of Solution A and Solution B.
Let's assume that we have 21 liters of Solution A and 4 liters of water, and 2 liters of Solution B and 3 liters of water.
Step 1: Calculate the total volume of the resultant mixture
The ratio of Solution A to Solution B is 5:6. Let's assume that the total volume of the resultant mixture is x liters.
Therefore, the volume of Solution A in the mixture is (5/11) * x liters, and the volume of Solution B in the mixture is (6/11) * x liters.
Step 2: Calculate the volume of alcohol in the resultant mixture
In Solution A, the alcohol-water ratio is 21:4, which means that there are 21/(21+4) = 21/25 liters of alcohol in every 25 liters of Solution A.
Similarly, in Solution B, the alcohol-water ratio is 2:3, which means that there are 2/(2+3) = 2/5 liters of alcohol in every 5 liters of Solution B.
Now, let's calculate the volume of alcohol in the resultant mixture.
For Solution A:
Volume of alcohol in Solution A = (21/25) * (5/11) * x liters
For Solution B:
Volume of alcohol in Solution B = (2/5) * (6/11) * x liters
Step 3: Calculate the percentage of alcohol in the resultant mixture
Total volume of alcohol in the mixture = Volume of alcohol in Solution A + Volume of alcohol in Solution B
Total volume of the mixture = Volume of alcohol in the mixture + Volume of water in the mixture
Therefore, the percentage of alcohol in the resultant mixture is:
(100 * Total volume of alcohol in the mixture) / Total volume of the mixture
Substituting the values, we have:
Percentage of alcohol in the resultant mixture = (100 * [((21/25) * (5/11) * x) + ((2/5) * (6/11) * x)]) / x
Simplifying the expression, we get:
Percentage of alcohol in the resultant mixture = (210/275) * 100
Percentage of alcohol in the resultant mixture ≈ 76.36%
Therefore, the correct answer is option C: 60%.
Let's assume that we have 21 liters of Solution A and 4 liters of water, and 2 liters of Solution B and 3 liters of water.
Step 1: Calculate the total volume of the resultant mixture
The ratio of Solution A to Solution B is 5:6. Let's assume that the total volume of the resultant mixture is x liters.
Therefore, the volume of Solution A in the mixture is (5/11) * x liters, and the volume of Solution B in the mixture is (6/11) * x liters.
Step 2: Calculate the volume of alcohol in the resultant mixture
In Solution A, the alcohol-water ratio is 21:4, which means that there are 21/(21+4) = 21/25 liters of alcohol in every 25 liters of Solution A.
Similarly, in Solution B, the alcohol-water ratio is 2:3, which means that there are 2/(2+3) = 2/5 liters of alcohol in every 5 liters of Solution B.
Now, let's calculate the volume of alcohol in the resultant mixture.
For Solution A:
Volume of alcohol in Solution A = (21/25) * (5/11) * x liters
For Solution B:
Volume of alcohol in Solution B = (2/5) * (6/11) * x liters
Step 3: Calculate the percentage of alcohol in the resultant mixture
Total volume of alcohol in the mixture = Volume of alcohol in Solution A + Volume of alcohol in Solution B
Total volume of the mixture = Volume of alcohol in the mixture + Volume of water in the mixture
Therefore, the percentage of alcohol in the resultant mixture is:
(100 * Total volume of alcohol in the mixture) / Total volume of the mixture
Substituting the values, we have:
Percentage of alcohol in the resultant mixture = (100 * [((21/25) * (5/11) * x) + ((2/5) * (6/11) * x)]) / x
Simplifying the expression, we get:
Percentage of alcohol in the resultant mixture = (210/275) * 100
Percentage of alcohol in the resultant mixture ≈ 76.36%
Therefore, the correct answer is option C: 60%.
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Solution A is made up of alcohol and water mixed in the ratio of 21:4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2:3 by volume. If Solution A and Solution B are mixed in the ratio of 5:6 by volume, what percent of the resultant mixture is alcohol?a)32.5%b)40%c)60%d)65%e)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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