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A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is
  • a)
    30%
  • b)
    40%
  • c)
    50%
  • d)
    60%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 20% ethanol solution is mixed with another ethanol solution, say, S...
Let the volume of the first and the second solution be 100 and 300.
When they are mixed, quantity of ethanol in the mixture
= (20 + 300S)
Let this solution be mixed with equal volume i.e. 400 of third solution in which the strength of ethanol is 20%.
So, the quantity of ethanol in the final solution
= (20 + 300S + 80) = (300S + 100)
It is given that, 31.25% of 800 = (300S + 100)
or, 300S + 100 = 250
or S = 1/2 = 50%
Hence, 50 is the correct answer.
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Most Upvoted Answer
A 20% ethanol solution is mixed with another ethanol solution, say, S...
To solve this problem, let's break it down into steps:

Step 1: Let's assume the volume of the 20% ethanol solution is x liters.
So, the volume of the unknown concentration ethanol solution S mixed with the 20% ethanol solution is 3x liters.

Step 2: When these two solutions are mixed, the total volume of the mixture becomes (x + 3x) = 4x liters.

Step 3: Now, let's find the amount of ethanol in the mixture before adding the equal volume of 20% ethanol solution.
The amount of ethanol in the 20% ethanol solution is 20% of x liters, which is (20/100) * x = 0.2x liters.
The amount of ethanol in the unknown concentration ethanol solution S is unknown, so let's call it s liters.
Therefore, the total amount of ethanol in the mixture before adding the equal volume of 20% ethanol solution is (0.2x + s) liters.

Step 4: After adding the equal volume of 20% ethanol solution, the total volume of the mixture becomes 2 * 4x = 8x liters.
The amount of ethanol in the equal volume of 20% ethanol solution is 20% of 4x liters, which is (20/100) * 4x = 0.8x liters.

Step 5: The total amount of ethanol in the resultant mixture is 31.25% of 8x liters, which is (31.25/100) * 8x = 2.5x liters.

Step 6: Now, let's set up an equation using the information we have:
0.2x + s + 0.8x = 2.5x

Step 7: Simplify the equation:
1x + s = 2.5x
s = 1.5x

Step 8: We know that the volume of the unknown concentration ethanol solution S mixed with the 20% ethanol solution is 3x liters.
Therefore, the concentration of S is (s/3x) * 100% = (1.5x/3x) * 100% = 50%.

Hence, the correct answer is option C, 50%.
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A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S isa) 30%b) 40%c) 50%d) 60%Correct answer is option 'C'. Can you explain this answer?
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