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A cask initially contains pure alcohol up to the brim. The cask can be

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A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 26 Dec 2015, 10:29
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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
plz explain someone
[Reveal] Spoiler: OA

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Re: A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 26 Dec 2015, 11:16
anik19890 wrote:
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
plz explain someone


Take these questions step by step.

You are given that the initial quantity of the cask is 15 l. So for the changing of the liquids,

The first time you remove 5 l of pure alcohol---> 10 l of alcohol remaining and you add 5 l of water. Ratio of alcohol in the remaining mixture = 10/(10+5) = 10/15 =2/3, similarly water = 1/3.

The second time you remove 5 l of the mixture having alcohol = 5*2/3 = 10/3 --> remaining alcohol = 10-10/3 =20/3

Similarly, the amount of water removed = 5*1/3=5/3 ---> remaining water = 5-5/3=10/3 but you also add 5 l more of water --> total water now = 5+10/3 = 25/3

Finally, ratio asked = 20/3 / 25/3 = 20/25 = 4/5

A is the correct answer.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1723 [0], given: 792

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Kudos [?]: 21 [0], given: 27

Re: A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 26 Dec 2015, 11:22
Engr2012 wrote:
anik19890 wrote:
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
plz explain someone


Take these questions step by step.

You are given that the initial quantity of the cask is 15 l. So for the changing of the liquids,

The first time you remove 5 l of pure alcohol---> 10 l of alcohol remaining and you add 5 l of water. Ratio of alcohol in the remaining mixture = 10/(10+5) = 10/15 =2/3, similarly water = 1/3.

The second time you remove 5 l of the mixture having alcohol = 5*2/3 = 10/3 --> remaining alcohol = 10-10/3 =20/3

Similarly, the amount of water removed = 5*1/3=5/3 ---> remaining water = 5-5/3=10/3 but you also add 5 l more of water --> total water now = 5+10/3 = 25/3

Finally, ratio asked = 20/3 / 25/3 = 20/25 = 4/5

A is the correct answer.


the second time when 5 l is removed why 5 is multiplied?

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Schools: Kellogg '18 (M)
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Re: A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 26 Dec 2015, 11:29
anik19890 wrote:
Engr2012 wrote:
anik19890 wrote:
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
plz explain someone


Take these questions step by step.

You are given that the initial quantity of the cask is 15 l. So for the changing of the liquids,

The first time you remove 5 l of pure alcohol---> 10 l of alcohol remaining and you add 5 l of water. Ratio of alcohol in the remaining mixture = 10/(10+5) = 10/15 =2/3, similarly water = 1/3.

The second time you remove 5 l of the mixture having alcohol = 5*2/3 = 10/3 --> remaining alcohol = 10-10/3 =20/3

Similarly, the amount of water removed = 5*1/3=5/3 ---> remaining water = 5-5/3=10/3 but you also add 5 l more of water --> total water now = 5+10/3 = 25/3

Finally, ratio asked = 20/3 / 25/3 = 20/25 = 4/5

A is the correct answer.


the second time when 5 l is removed why 5 is multiplied?


It's because you are told that 5 l of whatever is remaining in the cask is removed. Before the first one, the entire liquid was alcohol but now once we started to mix water with alcohol, whatever you remove now will be a mixture of water and alcohol. This mixture will have water and alcohol in the ratio determined by their ratio before the second one.

This is the reason why you have 5 l of mixture removed out of which 1/3 is water and 2/3 is alcohol.

Hope this helps
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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Re: A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 21 Jan 2017, 16:13
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Re: A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 17 Aug 2017, 00:46
Engr2012 wrote:
anik19890 wrote:
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
plz explain someone


Take these questions step by step.

You are given that the initial quantity of the cask is 15 l. So for the changing of the liquids,

The first time you remove 5 l of pure alcohol---> 10 l of alcohol remaining and you add 5 l of water. Ratio of alcohol in the remaining mixture = 10/(10+5) = 10/15 =2/3, similarly water = 1/3.

The second time you remove 5 l of the mixture having alcohol = 5*2/3 = 10/3 --> remaining alcohol = 10-10/3 =20/3

Similarly, the amount of water removed = 5*1/3=5/3 ---> remaining water = 5-5/3=10/3 but you also add 5 l more of water --> total water now = 5+10/3 = 25/3

Finally, ratio asked = 20/3 / 25/3 = 20/25 = 4/5

A is the correct answer.


Thanks for giving the solution.

However , I am confused how have you covered the condition "when the cask is fully emptied and filled to brim two times"

Doesn't the solution provided indicates that from cask 5lts solution is replaced with 5lts water twice.

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Re: A cask initially contains pure alcohol up to the brim. The cask can be [#permalink]

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New post 17 Aug 2017, 05:37
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Simplest solution: A is answer

Volume can = 15 Ltr initially full alcohol

1st mix = 5 ltr alcohol removed , 10 ltr remained

Volume Alcohol to Can is 10 /15

2nd Mix - Now 5 ltr mix is removed in that alcohol will be out by (10/15) * 5 = 10/3 ltr and remaining will be 10-10/3 = 20/3

Volume of Alcohol to can will be (20/3) / 15 = 4/9
means 4 is alcohol and 9 is mixture ( 4 ltr alcohol + 5 ltr water)

4/5 is the Answer A
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Re: A cask initially contains pure alcohol up to the brim. The cask can be   [#permalink] 17 Aug 2017, 05:37
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