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A container has a capacity of 20 gallons and is full of spi

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A container has a capacity of 20 gallons and is full of spi [#permalink] New post 22 Jan 2011, 02:22
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A container has a capacity of 20 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Nov 2013, 10:31, edited 1 time in total.
Edited the question.
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Re: Alligation Problem [#permalink] New post 22 Jan 2011, 09:43
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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: A container has a capacity of 200 gallons and is full of spi [#permalink] New post 22 Nov 2013, 10:27
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


sonuindia88 please correct question I think it should be 20 instead of 200
Cheers
J :)
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Re: A container has a capacity of 20 gallons and is full of spi [#permalink] New post 26 Mar 2014, 11:51
There is a direct formula to calculate such repetition:

Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:

Left QTY / 20 = (20 -4)^5 / 20^5

Left QTY = 20 (16/20)^5

Left QTY = 20 ( 4/5 )^5

Left QTY = 6.5536

Answer is B

But how to convert 4^6/5^4 to mixed fraction ?
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Re: A container has a capacity of 20 gallons and is full of spi [#permalink] New post 26 Mar 2014, 11:56
Expert's post
PiyushK wrote:
There is a direct formula to calculate such repetition:

Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:

Left QTY / 20 = (20 -4)^5 / 20^5

Left QTY = 20 (16/20)^5

Left QTY = 20 ( 4/5 )^5

Left QTY = 6.5536

Answer is B

But how to convert 4^6/5^4 to mixed fraction ?


4^6 = 2^12 = 4,096.
5^4 = 625.

\(\frac{4,096}{625}=6 \frac{346}{625}\).
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Re: A container has a capacity of 20 gallons and is full of spi [#permalink] New post 27 Mar 2014, 01:59
Good question, tough anf and tricky!
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Re: A container has a capacity of 20 gallons and is full of spi [#permalink] New post 20 Apr 2015, 17:48
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Re: A container has a capacity of 20 gallons and is full of spi   [#permalink] 20 Apr 2015, 17:48
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