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

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Question Stats: 71% (02:06) correct 29% (02:30) wrong based on 378 sessions

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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

Originally posted by marcodonzelli on 02 Mar 2008, 09:04.
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.
Veritas Prep GMAT Instructor V
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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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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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Director  Joined: 10 Sep 2007
Posts: 654
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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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

Director  Joined: 22 Nov 2007
Posts: 854
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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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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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 V
Joined: 02 Sep 2009
Posts: 59587
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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1
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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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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1
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: 7
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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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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Joined: 05 Mar 2015
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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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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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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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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
.8*10+w=[1-(.2*.25)](10+w)→
w=30 liters
C

Originally posted by gracie on 27 Jul 2017, 11:21.
Last edited by gracie on 19 Sep 2019, 20:08, edited 1 time in total.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3723
How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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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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How does one solve this using allegation approach? Bunuel, Abhishek009, VeritasPrepKarishma anyone?
Intern  B
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Posts: 1
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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Hi, why does this approach not work
20% of 10 litres of solution + x litres of water = 5% of (10+x) litres of solution

x being the added quantity of water
Intern  B
Joined: 28 Aug 2016
Posts: 11
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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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

We can back-solve as well:

20% of 10 liters is 2 liters.
20% reduced by 75% is 5%.

If we check C -> 30 + 10 (initial liters) = 40 liters, 2/40 = 1/20 or 5%
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Posts: 9850
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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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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

Concentration of alcohol = 20% = C1
A reduction by 75% means the concentration of alcohol should become 5% = Cavg
Concentration of alcohol in water = 0% = C2

10/w2 = (0 - 5) / (5 - 20) = 1/3

w2 = 30 lts

Check out the weighted avg blog to understand this:
https://www.veritasprep.com/blog/2011/0 ... -averages/
https://www.veritasprep.com/blog/2011/0 ... -mixtures/
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GMAT 1: 600 Q36 V31 Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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Trying to be consistent and use a table to solve all mixture problems. Having some trouble....Bunuel could you critique me on where i am going wrong:

Amount(L) Soln
20% (alcohol) 10 20(10)
100%(water) x 100x
5% (alcohol) 10 + x 5(10 + x)

20(10) + 100x = 5(10 +x)
200 - 50 +100x = 5x
150 = -95x

As mentioned above i see logically it is 150/5 = x........x= 30
Director  D
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How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

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FitnessforFriends wrote:
Trying to be consistent and use a table to solve all mixture problems. Having some trouble....Bunuel could you critique me on where i am going wrong:

Amount(L) Soln
20% (alcohol) 10 20(10)
100%(water) x 100x
5% (alcohol) 10 + x 5(10 + x)

20(10) + 100x = 5(10 +x)
200 - 50 +100x = 5x
150 = -95x

As mentioned above i see logically it is 150/5 = x........x= 30

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%

Hi FitnessforFriends
the above highlighted part should be
20(10) = 5(10 +x)

as the amount of alcohol remains same ...u have to calculate % of alcohol in new solution

thus 20(10) = 5(10 +x) ==> 200= 50+5x ==> 150/5=x===>30 hope it helps
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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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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

Intial= 10*0.20= 2Litres
Initial quantity of alcohol will remain in the solution but it will get diluted. As the concentration of alcohol in the solution is reduced by 75% means 25% of initial quantity of alcohol is present in the new solution which is equal to 2*0.25=1/2 litre=5%(as 2 litres of alcohol= 20%)

Final= (10+x)0.05
Initial quantity of alcohol in the solution=Final quantity of alcohol in the solution
2=(10+x)*0.05
200/5=10+x
40=10+x
X=30 Litres
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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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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

Alcohol = 20%*10 = 2 litres
If alcohol = 5%T= 2
T = 40 litres

Water to be added = 40-10=30 litres

IMO C

Posted from my mobile device Re: How much water should be added to 10 liters of a 20%-solution of alcoh   [#permalink] 25 Sep 2019, 19:04
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