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# How much water should be added to 10 liters of a 20%-solution of alcoh

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VP
Joined: 22 Nov 2007
Posts: 1079
How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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02 Mar 2008, 09:04
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How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?

A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Jul 2015, 10:24, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
Joined: 10 Sep 2007
Posts: 938
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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02 Mar 2008, 10:51
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In original Content of 10 litre, there is 2 litre alcohol and 8 litre water.

Question ask to reduce concentration of alcohol to 5% (reduce concentration from 20% by 75%).

So lets assume X litre water is added.

So alcohol remains 2, water is 8+X and total content is 10+X.

Now 2*100/(10+X) = 5 => X = 30

VP
Joined: 22 Nov 2007
Posts: 1079
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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02 Mar 2008, 10:58
abhijit_sen wrote:
In original Content of 10 litre, there is 2 litre alcohol and 8 litre water.

Question ask to reduce concentration of alcohol to 5% (reduce concentration from 20% by 75%).

So lets assume X litre water is added.

So alcohol remains 2, water is 8+X and total content is 10+X.

Now 2*100/(10+X) = 5 => X = 30

very quickly: 2/(10+x)=1/20, x=30
Manager
Joined: 10 Mar 2014
Posts: 245
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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22 Jul 2015, 09:34
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
 25 liters
 27 liters
 30 liters
 32 liters
 35 liters

Hi Bunuel,

Could you please clarify 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75%?. I am getting confusion in this term.

Regards
Math Expert
Joined: 02 Sep 2009
Posts: 39672
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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22 Jul 2015, 10:27
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PathFinder007 wrote:
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
 25 liters
 27 liters
 30 liters
 32 liters
 35 liters

Hi Bunuel,

Could you please clarify 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75%?. I am getting confusion in this term.

Regards

The question asks about the amount of water we should add to 10 liters of a 20%-solution of alcohol for the solution to become 5%-solution of alcohol (20% reduced by 75% is 5%).
_________________
Intern
Joined: 02 Mar 2015
Posts: 4
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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22 Jul 2015, 13:08
The quantity of alcohol in the actual mixture is 2 litres (20% of 10 litres). Now it is said that the concentration is reduced by 75% or 3/4th of 20% which is 5%. Now in the new mixture this 2 litres alcohol is 5% of the total mixture therefore the total mixture would be 2 *20=40 litres. So 30 litres is added. (Note 5% is 1/20)
Intern
Joined: 11 Dec 2013
Posts: 8
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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26 Jul 2015, 22:46
sudipnayak93 wrote:
The quantity of alcohol in the actual mixture is 2 litres (20% of 10 litres). Now it is said that the concentration is reduced by 75% or 3/4th of 20% which is 5%. Now in the new mixture this 2 litres alcohol is 5% of the total mixture therefore the total mixture would be 2 *20=40 litres. So 30 litres is added. (Note 5% is 1/20)

10 litres is containing 20% alcoholol...means 2 litres of alcohol and 8 litres of water.
Now the alchol percentage is to reduced by 75%..that means 75% of 20%...that means in the new solution, the content of alcohol should be 5%. (Reduction of 15%).
So that means, the 2 litres of alcohol will make 5% of new solution..
5%-->2 litres
100%-->40 litres..
That means an additional 30 litres (10 litres was initial solution)...and this additional 30 litres is only water.
To cross check--> in new solution..40 litres , 2 litres is alcohol and 38 litres is water.
2 litres = 5% and 38 litres=95%.

Regards
Naresh
Director
Joined: 05 Mar 2015
Posts: 931
Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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02 May 2016, 10:12
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?

A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters

Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=10+x)))

2=5%*(10+x)-------->x=30
Ans C
Re: How much water should be added to 10 liters of a 20%-solution of alcoh   [#permalink] 02 May 2016, 10:12
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