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A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5

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bmwhype2
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A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   Updated on: 25 Oct 2014, 06:19
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A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%
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D

Originally posted by bmwhype2 on 24 Nov 2007, 02:18.
Last edited by Bunuel on 25 Oct 2014, 06:19, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   24 Nov 2007, 15:11
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I disagree

50L * .05 = 2.5 L of alc, 50L - 2.5L = 47.5L of water

2.5 + 1.5 = 4L of alcohol in new solution

47.5L + 8.5L = 56L of water

4L / 56L = 1/14

this is ~7%
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   30 Nov 2007, 11:39
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GMAT TIGER wrote:
bmwhype2 wrote:
A 50 liter solution of alcohol and water is 5% alcohol. If 1.5 liters of alcohol and 8.5 liters are added to the solution, what percent of the solution produced is alcohol?


= 4/60
= 1/15
= 6.67%


5% of 50 = 2.5 liters of alcohol

10 liters added
50+10=60

2.5+1.5=4

4/60=2/30=1/15=6.67%
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   24 Nov 2007, 02:44
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bmwhype2 wrote:
A 50 liter solution of alcohol and water is 5% alcohol. If 1.5 liters of alcohol and 8.5 liters are added to the solution, what percent of the solution produced is alcohol?


= 4/60
= 1/15
= 6.67%
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   24 Nov 2007, 15:25
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C1=Va/(Va+Vw) where, C -concentration; Va - volume of alcohol, Vm - volume of water. Vtotal=(Va+Vw) - total volume.

C1=Va/(Va+Vw)

C2=(Va+dVa)/(Va+Vw+dVa+dVw) where dVa - additional volume of alcohol, dVm - additional volume of water

C2=(C1*Vtotal+dVa)/(Vtotal+dVa+dVw)

C2=(0.05*50+1.5)/(50+1.5+8.5)=4/60=1/15~0.06666666 ==>6,(6)%
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   02 Apr 2016, 14:00
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let x=% of alcohol in final solution
2.5+1.5=60x
x=1/15=6 2/3%
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   30 Nov 2007, 11:40
Dakinemon wrote:
I disagree

50L * .05 = 2.5 L of alc, 50L - 2.5L = 47.5L of water

2.5 + 1.5 = 4L of alcohol in new solution

47.5L + 8.5L = 56L of water

4L / 56L = 1/14

this is ~7%


u took the percentage of alcohol from total water
Q asked for percentage of alcohol from total solution
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   02 Apr 2016, 12:19
5% alcohol in 50 litre solution = 2.5 litres
adding 1.5 litres to it makes it total of 4 litres
total solution = 60 litres
% alcohol = 4/60 * 100 = 6.666667%
Answer - D
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   23 Jun 2017, 15:11
I am not clear on this question, shouldn't the answer be 7%?

As new solution will be 4 Ltrs Alcohol & 56 Ltrs of Water = 60 in Total

\(4/60*100 = 6.66\)

Please advise if you I am going wrong here?

Bunuel, Abhishek009 - Please advise
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   23 Jun 2017, 15:34
ydmuley

A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution,
what percent of the solution produced is alcohol?

we are asked to find the exact percent- why are you rounding off the value?

\(\frac{4}{60}\) * 100 = \(\frac{20}{3}\) = 6 \(\frac{2}{3}\) = Ans is D
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A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   23 Jun 2017, 15:35
bmwhype2 wrote:
A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%


Solution \(= 50\) liters

Alcohol is 5% of 50 \(= \frac{5}{100} * 50 = 2.5\) liters

1.5 liters of alcohol added. Therefore Total liters of alcohol \(= 2.5 + 1.5 = 4\) liters.

1.5 liters of alcohol and 8.5 liters of water is added to solution \(= 50 + 1.5 + 8.5 = 60\) liters.

Percentage of alcohol in new solution \(= \frac{4}{60} * 100 = 66.67\)% or \(6 \frac{2}{3}\) % . Answer (D) ...
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   23 Jun 2017, 15:40
sashiim20 wrote:
bmwhype2 wrote:
A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%


Solution \(= 50\) liters

Alcohol is 5% of 50 \(= \frac{5}{100} * 50 = 2.5\) liters

1.5 liters of alcohol added. Therefore Total liters of alcohol \(= 2.5 + 1.5 = 4\) liters.

1.5 liters of alcohol and 8.5 liters added to solution \(= 50 + 1.5 + 8.5 = 60\) liters.

Percentage of alcohol in new solution \(= \frac{4}{60} * 100 = 66.67\)% or \(6 \frac{2}{3}\) % . Answer (D) ...


Once again thanks for the explanation, it was helpful. Where I went wrong is incorrectly reading option C & D as \(62/3\) and \(61/3\)

Hence, I was left with option E which was more closer to the number.

Good one :-D
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   23 Jun 2017, 15:44
Leo8 wrote:
ydmuley

A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution,
what percent of the solution produced is alcohol?

we are asked to find the exact percent- why are you rounding off the value?

\(\frac{4}{60}\) * 100 = \(\frac{20}{3}\) = 6 \(\frac{2}{3}\) = Ans is D



Got it Leo8 - Thank you. I misread the answer choices as 61/3 & 62/3
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   19 Sep 2020, 08:22
bmwhype2 wrote:
A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 liters of alcohol and 8.5 liters of water are added to this solution, what percent of the solution produced is alcohol?

A. 5.5%
B. 6%
C. 6 1/3%
D. 6 2/3%
E. 7%


presently out of 50 ltrs alcohol is 2.5 ltrs and 47.5 ltrs water
later 1.5 ltrs alcohol added ana 8.5 ltrs water added
4 ltrs alcohol and 56 ltrs water
4/60 ; 1/15 ; ~6.66%
option D
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   20 Oct 2020, 12:17
= 4/60
= 1/15
= 6.67%

Answer is D.
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   07 Aug 2023, 01:07
Can anyone solve this by alligation method?
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   17 Aug 2023, 09:06
I used a table to solve this.

..............Original......+Alcohol.....+Water.....Final

Alcohol....2.5 lit...........1.5l.............0l.........4l

Water......47.5 lit.........0l................8.5l.......56l

Total.......50 lit............1.5l.............8.5l........60l

Now, we just divide 4 by 60, to get 6.67%.

Thus, answer is D.
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink] New post   18 Aug 2023, 05:01
Expert Reply
Anki111 wrote:
Can anyone solve this by alligation method?


We have a 50 ltr solution or 5% alcohol.
If we add 1.5 ltr alcohol and 8.5 ltr water, it means we are adding a 10 ltr solution of 15% alcohol (because concentration of alcohol is 1.5/10 = 15%)

Use the scale method:

5% -------------------------- 15%
(50).................................(10)

The 10% distance between 5% and 15% is divided in the ratio 1:5 so \(Cavg = 5 + (\frac{1}{6})*10 = 6(\frac{2}{3})\)%

Answer (D)

Check out these videos on how to use the scale method and how to apply it to mixtures:
https://www.youtube.com/watch?v=_GOAU7moZ2Q
https://www.youtube.com/watch?v=VdBl9Hw0HBg

and these posts:
https://anaprep.com/arithmetic-weighted-averages/
https://anaprep.com/arithmetic-mixtures/
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Re: A 50-liter solution of alcohol and water is 5 percent alcohol. If 1.5 [#permalink]
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