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Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is
- a)94%
- b)92%
- c)90%
- d)89%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two alcohol solutions, A and B, are mixed in the proportion 1:3 by vol...
Let the quantity of solutions A and B mixed initially be p and 3p respectively. After an additional 4p of solution A is added 60% of (1 p + 4 p) + x% of 3 p = 72% of (1p + 4p + 3p) ⇒ x = 92
Most Upvoted Answer
Two alcohol solutions, A and B, are mixed in the proportion 1:3 by vol...
Solution:
Let's assume that the initial volumes of solutions A and B are x and y respectively.
First Mixture:
- The proportion of alcohol in solution A is 60%, so the volume of alcohol in solution A is 0.6x.
- The proportion of alcohol in solution B is unknown, so let's assume it to be p%. The volume of alcohol in solution B is py/100.
When the two solutions are mixed in the ratio 1:3, the volume of solution A becomes x/4 and the volume of solution B becomes 3y/4.
Second Mixture:
- The volume of the mixture is then doubled by adding solution A. So, the volume of solution A added is x/2 and the volume of solution B remains the same, i.e., 3y/4.
- The resulting mixture has 72% alcohol, which means the volume of alcohol in the resulting mixture is 72% of the total volume of the mixture.
Now, let's calculate the volume of alcohol in the resulting mixture:
- The volume of alcohol in solution A is 0.6x.
- The volume of alcohol in solution B is py/100.
- The volume of alcohol in the resulting mixture is 72% of the total volume of the mixture.
The total volume of the mixture is (x/2) + (3y/4).
Therefore, the equation becomes:
0.6x + (py/100) = 0.72 * [(x/2) + (3y/4)]
Simplifying the equation:
0.6x + (py/100) = 0.36x + 0.54y
Multiply both sides of the equation by 100 to eliminate the fractions:
60x + py = 36x + 54y
Rearranging the equation:
24x - 54y = py - 36x
24x + 36x = 54y + py
60x = 90y
Simplifying further:
2x = 3y
Now, we have the equation 2x = 3y, which tells us that the initial volumes of solutions A and B are in the ratio 2:3. Since the initial proportion of alcohol in solution A is 60%, the proportion of alcohol in solution B is 100% - 60% = 40%.
Therefore, the percentage of alcohol in solution B is 40%, which corresponds to option B.
Let's assume that the initial volumes of solutions A and B are x and y respectively.
First Mixture:
- The proportion of alcohol in solution A is 60%, so the volume of alcohol in solution A is 0.6x.
- The proportion of alcohol in solution B is unknown, so let's assume it to be p%. The volume of alcohol in solution B is py/100.
When the two solutions are mixed in the ratio 1:3, the volume of solution A becomes x/4 and the volume of solution B becomes 3y/4.
Second Mixture:
- The volume of the mixture is then doubled by adding solution A. So, the volume of solution A added is x/2 and the volume of solution B remains the same, i.e., 3y/4.
- The resulting mixture has 72% alcohol, which means the volume of alcohol in the resulting mixture is 72% of the total volume of the mixture.
Now, let's calculate the volume of alcohol in the resulting mixture:
- The volume of alcohol in solution A is 0.6x.
- The volume of alcohol in solution B is py/100.
- The volume of alcohol in the resulting mixture is 72% of the total volume of the mixture.
The total volume of the mixture is (x/2) + (3y/4).
Therefore, the equation becomes:
0.6x + (py/100) = 0.72 * [(x/2) + (3y/4)]
Simplifying the equation:
0.6x + (py/100) = 0.36x + 0.54y
Multiply both sides of the equation by 100 to eliminate the fractions:
60x + py = 36x + 54y
Rearranging the equation:
24x - 54y = py - 36x
24x + 36x = 54y + py
60x = 90y
Simplifying further:
2x = 3y
Now, we have the equation 2x = 3y, which tells us that the initial volumes of solutions A and B are in the ratio 2:3. Since the initial proportion of alcohol in solution A is 60%, the proportion of alcohol in solution B is 100% - 60% = 40%.
Therefore, the percentage of alcohol in solution B is 40%, which corresponds to option B.
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Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B isa)94%b)92%c)90%d)89%Correct answer is option 'B'. Can you explain this answer?
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