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

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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.

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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

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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

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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

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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%).
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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)

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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

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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
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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

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Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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26 Jul 2017, 22:37
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Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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26 Jul 2017, 23:05
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

Originally, the solution had 2L of alcohol and 8L of water. To reduce the concentration of alcohol by 75% means to bring down the alcohol level to 2L * 25% = 0.5L, so that the solution would contain 9.5L water and 0.5L alcohol.

$$\frac{8+x}{10+x} = \frac{95}{100}$$

$$800 + 100x = 950 + 95x$$

$$5x = 150$$

$$x = 30$$. Ans - C.
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How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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27 Jul 2017, 11:21
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 w=amount of water to be added
.2*10=.05(10+w)
w=30 liters
C

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

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30 Jul 2017, 12:55
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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

One iteration of a weighted average equation here is
(Concentration of A)(Vol A) + (Concen of B)(Vol B) = (Desired Concen)(Total vol = A+B)

This question is a bit unusual.

First, often, the desired concentration is given. Second, it might be hard to discern which value to reduce by 75 percent. In the equation above for this question,

A = 10 liters of soltion with 20% (=.20) alcohol
B = x liters of water with 0% (=0.0) alcohol

If water is zero percent alcohol, its percentage can't be reduced any further. The question therefore asks that 20 percent concentration be reduced by 75 percent:

(.20)(.25) = .05. The latter is the desired concentration of resultant solution.

In the equation, you don't have to insert second term on LHS. Doing so just makes clear that you are adding x, but its concentration of alcohol has no weight. So

(.20)10 + (0)x = (.05)(10 + x)

2 + 0x = .5 + .05x

1.5 = .05x

$$\frac{1.5}{.05}$$= x

x = 30

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Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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18 Sep 2017, 22:28
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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

Responding to a pm:

Right now, we have a 20% solution of alcohol.
We need to reduce the concentration of alcohol by 75% i.e. reduce it by 15% to make it 5%.

So now, you have a 10 lt solution of 20% alcohol and you want to make it 5% alcohol by adding pure water (i.e. 0% alcohol)

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (0 - 5)/(5 - 20) = 1/3

So for every 1 lt of original solution, you need 3 lt of water. So for 10 litres of original solution, you need 30 lt of water.

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Re: How much water should be added to 10 liters of a 20%-solution of alcoh [#permalink]

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28 Sep 2017, 09:31
How does one solve this using allegation approach? Bunuel, Abhishek009, VeritasPrepKarishma anyone?

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Re: How much water should be added to 10 liters of a 20%-solution of alcoh   [#permalink] 28 Sep 2017, 09:31
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