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August 7th, 2019, 07:56 AM   #11
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Quote:
Originally Posted by skipjack View Post
The sherry is 15% spirit, but the spirit can't be removed by itself.
Still I can't understand why are you changing 300 units to 100 or 200.

Please explain in simple English, otherwise explain with another example.
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August 7th, 2019, 09:03 AM   #12
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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 ultra-short solution could be (15 - 9)/(15 - 6) = 6/9 = 2/3.
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August 7th, 2019, 11:07 AM   #13
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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 (1-x)*0.15 + (x)*0.06. We are told this is equal to 1*0.09.

(1-x)*0.15 + x*0.06 = 0.15 - x*0.09 = 0.09
-> x = 0.06/0.09 = 2/3
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August 8th, 2019, 07:04 AM   #14
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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.
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August 8th, 2019, 08:35 AM   #15
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Multiplying the overall volume by the concentration of spirit gives the volume of spirit.
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August 8th, 2019, 02:23 PM   #16
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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.
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File Type: png Screenshot 2019-08-09 at 10.23.11 AM.png (13.0 KB, 1 views)

Last edited by skipjack; August 8th, 2019 at 09:27 PM.
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