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14 Jul 2023, 02:18
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B
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Difficulty:
45%
(medium)
Question Stats:
71% (01:43) correct
29%
(01:47)
wrong
based on 221
sessions
History
Date
Time
Result
Not Attempted Yet
A butler stole wine from a cask that initially held a wine containing 12% alcohol. He then replaced the stolen wine with one that only contained 6% alcohol. As a result, the alcohol concentration in the wine within the cask decreased to 8%. What proportion of the original wine in the cask did the butler steal?
A. 1/3
B. 2/3
C. 3/4
D. 7/11
E. 9/13
A. 1/3
B. 2/3
C. 3/4
D. 7/11
E. 9/13
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14 Jul 2023, 02:40
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Bunuel
We can use teeter - totter method (concept of weighted averages) to solve this question.
Attachment:
Screenshot 2023-07-14 151854.jpg [ 17.01 KiB | Viewed 3641 times ]
Had the cask contained an equal volume of 12% alcohol and 6% alcohol then the concentration of alcohol in that cask would be 9%. However, the concentration of alcohol in the cask is 8%. Hence, we can infer that the cask has a greater quantity of 6% alcohol than of 12% alcohol.
The ratio of 12% Alcohol to 6% Alcohol in the cask with 8% alcohol = \(\frac{2}{4}\)
Therefore, the 8% cask has 2 parts of 6% alcohol and 1 part of 12% alcohol.
Hence, the butler stole 2 parts of the 12% wine, which the butler then replaced with the 6% wine, and, only 1 part of the 12% wine was left in the cask.
Proportion of the original wine that was stolen = \(\frac{2}{3}\)
Option B
14 Jul 2023, 04:08
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allegation method :
----6 -- 8
-----12
--4-----6
4:6 ; 2:3
option B
----6 -- 8
-----12
--4-----6
4:6 ; 2:3
option B
Bunuel
