MixtureQ

[kpkanupriyakhmi]

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) 1 : 2
(B) 2 : 1
(C) 1 : 1
(D) 4 : 5
(E) 5 : 4
how to do such Q and I could not even visualize the Q.
Please reply ASAP.

[tommywallach]

Hey KP,

The question is badly worded. What they mean is that the cask has 5 liters removed and is refilled again twice.

So we remove 5 liters of alcohol and put in 5 liters of water. Now we have:

10 liters of alcohol
5 liters of water

Now we remove 5 liters again. That 5 liters is 2/3 alcohol and 1/3 water, so 3 and a 1/3 liters alcohol, 1 and 2/3 liters water. Now we have:

6 and 2/3 liters alcohol
3 and 1/3 liters water

Now we put in another 5 liters of water. Our final tally is:

6 and 2/3 liters alcohol
8 and 1/3 liters water

That's a ratio of 4 to 5.

-t

[kpkanupriyakhmi]

What can be the level of Mixture Questions on the test?

[tommywallach]

All categories can be of any difficulty level, as far as I know. (Though it's difficult to write a VERY easy combinatorics question...)

-t