A brown flask contains a concoction that is 20% alcohol. A red flask

Question

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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Official Answer

C

(A) 23%

(B) 25%

(C) 32%

(D) 33%

(E) 40%

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divyadna · Accepted Answer

Please find the solution by alligation method.

Posted from my mobile device

Nidzo · Answer

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

kungfury42 · Answer

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

gonbondulich · Answer

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

DrHuber · Answer

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%.

AdiGoyal2022 · Answer

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%

A brown flask contains a concoction that is 20% alcohol. A red flask

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A brown flask contains a concoction that is 20% alcohol. A red flask

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