August 7th, 2019, 07:56 AM  #11 
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1  
August 7th, 2019, 09:03 AM  #12 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
When some of the sherry is stolen, the volume of the sherry in the butt changes. When the stolen sherry is replaced with wine, the butt's contents is restored to its original volume. For convenience, I took the remaining volume of sherry just after the theft to be 100 units. These 100 units contained 15 units of spirit. If 100r units of sherry were stolen, adding 100r units of wine that is 6% spirit creates a total volume of 100(1 + r) units, and the new volume of spirit is (15 + 6r) units. As the final spirit concentration is 9%, 15 + 6r = 9(1 + r), which implies r = (15  9)/(9  6) = 2. Hence the butler stole 200 units of sherry from an original 300 units of sherry, i.e. 2/3 of the original volume of sherry. The ultrashort solution could be (15  9)/(15  6) = 6/9 = 2/3. 
August 7th, 2019, 11:07 AM  #13 
Senior Member Joined: Jun 2019 From: USA Posts: 288 Thanks: 147 
Would a picture help? Let x be the fraction of the sherry that he stole. After he refills it with the 6 % solution, then the fraction of the butt containing alcohol is (1x)*0.15 + (x)*0.06. We are told this is equal to 1*0.09. (1x)*0.15 + x*0.06 = 0.15  x*0.09 = 0.09 > x = 0.06/0.09 = 2/3 
August 8th, 2019, 07:04 AM  #14 
Senior Member Joined: Aug 2014 From: India Posts: 473 Thanks: 1 
Why are you multiplying volume & concentration like x*0.06 or (1 x)*0.15? What do I get if I multiply volume & concentration? Last edited by skipjack; August 8th, 2019 at 08:33 AM. 
August 8th, 2019, 08:35 AM  #15 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
Multiplying the overall volume by the concentration of spirit gives the volume of spirit.

August 8th, 2019, 02:23 PM  #16 
Senior Member Joined: Mar 2019 From: TTF area Posts: 168 Thanks: 1 
The working: According to the rule of alligation, Therefore, Required ratio = 3 : 6 = 1 : 2 Clearly, 1/3 of the butt of sherry was left. It means the butler stole 2/3 of the butt. Last edited by skipjack; August 8th, 2019 at 09:27 PM. 

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