A cask initially contains pure alcohol up to the brim. The cask can be emptied by removing exactly 5 liters at a time . Each time this is done, the cask must be filled back to the brim with water. The capacity of the cask is 15 liters. When the cask is completely emptied and filled back to the brim two times, what is the ratio of alcohol to water in the cask
A. 4/5
B. 3/5
C. 4/6
D. 3/6
E. 2/6
Initial Amount of Alcohol = 15 Liters
After removing 5 liters of alcohol, amount left = 10 liters
Now, 5 liters of water is added hence \(\frac{1}{3}rd\) volume of 15 liters is water.
Again cask is emptied by 5 liters(mix of alcohol and water) and 5 liters of water is added.
Hence total water portion now = \(\frac{1}{3}*10 + 5 = \frac{25}{3}\)
Alcohol portion = \(15 - \frac{25}{3} = \frac{20}{3}\)
Ratio of alcohol to water = \(\frac{20}{3}:\frac{25}{3} = \frac{4}{5}\)
IMO Answer D.
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