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TJ · Joined: 06 Sep 2003 Posts: 2

a dishonest barman removes 3litres of wine from a barrel, replacing them with water and mixing the contents. he repeats the theft twice more, removing 9litres in total and replacing them with water. As a result the wine remaining in the barrel is half its original strength. how much wine was there at the start?

Saphira · Joined: 19 Nov 2003 Posts: 7

18 litres

ae_los3r · Joined: 23 May 2005 Posts: 5

My guess would be 18 lts as well, but this stinks of a trick question.

realistic_david · Joined: 19 Apr 2004 Posts: 1

is it 18? if its half the strength then it be 9 x 2

BoomBoom · Joined: 06 Mar 2005 Posts: 8

I would guess a barrel full or just about 18 litres... but maybe I'm wrong... check it out, "remmoving 9L in all and replacing the 9L with water...half it's original strength", double up 9 L which makes 18L.

Gregg · Joined: 05 Jun 2007 Posts: 5

18 liters of wine at the start...if you say 18 liters is at original strength then you want to make that 18 liters half strength you would remove 9 liters of wine and replace it with water =)

Noodles · Joined: 27 Mar 2006 Posts: 4

PeterD · Joined: 17 Jun 2004 Posts: 3

The answer is approximately 14.54196631 litres.The formula is 3/(1-1/(2^(1/3)))After the first time, you aren't removing 3 litres of full strength wine. Each time, you are removing a fixed percentage, rather than a fixed amount.

bigmary2 · Joined: 03 Sep 2006 Posts: 6

Ooh, hard.Original volume = x. Barman removes 3l, volume of wine remaining = x-3.Barman adds 3l water, therefore concentration of wine = (x-3)/x.Barman removes another 3l, OF WHICH 3(x-3)/x is wine.Volume of wine now remaining = x - 3 - 3(x-3)/xBarman now tops wine up, concentration = 1/x [x-3 - 3(x/3)/x]Barman removes another 3l, of which 3[ 1/x {x-3 - 3(x/3)/x} ] is wine.Volume of wine now remaining = x - 3 - 3(x-3)/x - 3[ 1/x {x-3 -3(x/3)/x} ]Concentation is now (x - 3 - 3(x-3)/x - 3[ 1/x {x-3 -3(x/3)/x} ] )/x = 0.5Multiplying out:1 - 6/x + 9/x^2 - 3/x + 9/x^2 +9/x^2 - 27/x^3 = 0.5Multiply through by x^30.5 x^3 - 9x^2 + 27x - 27 = 0.This is now a cubic equation, for which the only real (non-complex) root is (approximately) 14.541966, or3 / (1 - 1/(cuberoot 2))