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Alligation Problem

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Alligation Problem [#permalink]

22 Jan 2011, 03:22

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A container has a capacity of 200 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find how much spirit is left in the resulting mixture finally?

a) 6(257/525) gallons b) 6(346/625) gallons

c) 6.5 gallons d)6.25 gallons

e) None of these

Please solve through alligation or short cut process....

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Re: Alligation Problem [#permalink]

22 Jan 2011, 10:43

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sonuindia88 wrote:

A container has a capacity of 200 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find how much spirit is left in the resulting mixture finally?

a) 6(257/525) gallons
b) 6(346/625) gallons
c) 6.5 gallons
d) 6.25 gallons
e) None of these

First of all I think it should be 20 gallons instead of 200 in order the answer to be B.

Note that 4 gallons is 20% of a capacity. Now, when we remove 20% of spirit for the first time 80% of spirit is left --> when we remove 4 gallons of the mixture for the second time, or again 20% of the capacity, we still remove 20% of the remaining spirit with it (this 4 gallons of the mixture, which is 20% of the capacity, contains 20% of the remaining spirit), so again 80% of the spirit is left... So every time we remove 4 gallons, we re move 20% of the remaining spirit and 80% is left. So after 5 removals there will be 20*0.8^5 gallons of spirit left: 20*(\frac{4}{5})^5=\frac{4^6}{5^4}= 6\frac{346}{625}.

Answer: B.

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Re: Alligation Problem [#permalink] 22 Jan 2011, 10:43

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