
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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August 5th, 2019, 07:43 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1  explain this question clearly.
A butler stole wine from a butt of sherry which contains 15% of spirit and he replaced what he had stolen by wine containing 6% of spirit. The butt was then 9% strong only. How much of the butt did he steal? I didn't understand the question, Is my understanding correct? he stole wine which has 15% spirit and withdrew some wine and pour wine which has 6% spirit. Now spirit concentration is 9%. What should I find? I didn't understand this final part: How much of the butt did he steal? Last edited by Ganesh Ujwal; August 5th, 2019 at 07:45 PM. 
August 5th, 2019, 08:23 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
The butt originally contained 45 units of spirit in 300 units of "mixture". The butler stole 30 units of spirit in 200 units of mixture (2/3 of the butt's contents), leaving 15 units of spirit in 100 units of mixture. He then added 12 units of spirit in 200 units of wine, so there were now 27 units of spirit in 300 units of (adulterated) "mixture" (a 9% concentration of spirit). 
August 6th, 2019, 08:07 AM  #3  
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1  Quote:
Why are you changing total units of mixtures if it is constant? Last edited by Ganesh Ujwal; August 6th, 2019 at 08:10 AM.  
August 6th, 2019, 10:54 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
The question's wording could be clearer. It says the butler stole wine from a butt of sherry. I assumed that he stole sherry from the butt without altering the percentage of spirit in the remaining sherry. I referred to the sherry as "mixture". I showed that (with the above assumptions) the rest of the question would make sense if the butler stole 2/3 of the butt's contents, leaving 100 units of the original 300 units. Those remaining 100 units would have contained 15 units (15% of 100 units) of spirit. 
August 6th, 2019, 09:27 PM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1 
If he stole 30 units of spirit how much mixture units leftover?

August 6th, 2019, 11:25 PM  #6 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
see post #2, 2nd line

August 6th, 2019, 11:51 PM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1  
August 7th, 2019, 01:48 AM  #8 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
30 units of spirit is 200 units of 15% wine.

August 7th, 2019, 05:33 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1  
August 7th, 2019, 05:57 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
The sherry is 15% spirit, but the spirit can't be removed by itself.


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