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Difficulty:
45%
(medium)
Question Stats:
73% (02:10) correct
27%
(02:31)
wrong
based on 918
sessions
History
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A brown flask contains a concoction that is 20% alcohol. A red flask contains a concoction with an unknown amount of alcohol. An equal amount of both flasks is poured into an empty jug. If the resulting mixture has an alcohol concentration that is 30% greater than the alcohol concentration of the brown flask, what percent alcohol did the red flask originally contain?
(A) 23%
(B) 25%
(C) 32%
(D) 33%
(E) 40%
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(A) 23%
(B) 25%
(C) 32%
(D) 33%
(E) 40%
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Anki111
Please find the solution by alligation method.
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The resulting mixture will have \(20*1.3 = 26\)
As we are mixing both mixtures equally, the average of the two will be 26%.
Let the alcohol content is the red flask be x.
\(\frac{20+x}{2} = 26\)
\(20 + x = 52\)
\(x = 32\)
Answer C
As we are mixing both mixtures equally, the average of the two will be 26%.
Let the alcohol content is the red flask be x.
\(\frac{20+x}{2} = 26\)
\(20 + x = 52\)
\(x = 32\)
Answer C
General Discussion
kungfury42
Joined: 07 Jan 2022
Last visit: 31 May 2023
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A nice trap option would've been 80 because that's what I set out to look for after a quick skim through of the question, and I believe many might commit the same error 
However, a detailed examination revealed that the final mixture is 30% more concentrated than the one in brown flask. Note that it is 30% and not 30 % points.
So if the brown flask has a 20% strong solution, the final mixture will be 20*1.3=26% strong.
And since we're mixing equal quantities of the brown flask and the red flask, 26 must be the average of 20 and x where x is the strength of the solution in red flask and equals 32.
Hence, option C.
Posted from my mobile device
However, a detailed examination revealed that the final mixture is 30% more concentrated than the one in brown flask. Note that it is 30% and not 30 % points.
So if the brown flask has a 20% strong solution, the final mixture will be 20*1.3=26% strong.
And since we're mixing equal quantities of the brown flask and the red flask, 26 must be the average of 20 and x where x is the strength of the solution in red flask and equals 32.
Hence, option C.
Posted from my mobile device
Posts: 1
Bunuel why its 32 instead of 33?. The exercise says it has an alcohol concentration greater than 30% (ie. greater than 26%). So if its 32, it would equal 26,but not gonna be greater.
Thanks
Thanks
To solve this problem, we can use the following equation:
0.2A + x = 1.3(0.2A) where A is the amount of liquid in the brown flask, x is the amount of alcohol in the red flask, and 1.3(0.2A) is the alcohol concentration of the resulting mixture.
Simplifying this equation, we get: x = 0.26A
This means that the red flask originally contained 26% alcohol. Therefore, the answer is (C) 32%.
0.2A + x = 1.3(0.2A) where A is the amount of liquid in the brown flask, x is the amount of alcohol in the red flask, and 1.3(0.2A) is the alcohol concentration of the resulting mixture.
Simplifying this equation, we get: x = 0.26A
This means that the red flask originally contained 26% alcohol. Therefore, the answer is (C) 32%.
Posts: 1
The problem statement says 30% greater not greater than 30%, both are very different in their meaning where the former means greater by 30% and the latter means greater than 30%
gonbondulich
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