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# The ratio of alcohol and water in three mixtures of alcohol and water

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8883
Location: Pune, India
The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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15 Feb 2016, 20:28
2
9
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:45) correct 23% (02:31) wrong based on 261 sessions

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The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?
A)65%
B)70%
C)75%
D)80%

Solution:

With 3 quantities, the most straight forward method would be our usual weighted average formula.
We can use the scale method on two quantities at a time.
Here, I say that solution 1 has 3/5 alcohol and solution 2 has 4/5 alcohol. When we mix 1 part of each, we will get a mixture with 3.5/5 alcohol (it's simple average because both solutions are mixed in equal quantities).

3.5/5 = 7/10

Solution 3 has 7/10 alcohol.

2 parts of previous mix is mixed with 1 part of solution 3 but both have 7/10 alcohol. So the total mixture will have 7/10 = 70% alcohol.

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Karishma
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Joined: 14 Feb 2016
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Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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15 Feb 2016, 21:12
5
3
VeritasPrepKarishma wrote:
Quote:
The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?
A)65%
B)70%
C)75%
D)80%

how can the following problem be solved using the scale/ratio formula method?

The ratios are given such that the sum of alcohol and water can be brought up to 10 for each mixture. (Since equal quantities are to be added)
For 3:2 lets take 6 parts alcohol and 4 parts water
For 4:1 lets take 8 parts alcohol and 2 parts water
For last since the sum is already 10, 7 parts alcohol and 3 parts water.

Mixing these three will give 6+8+7 =21 units alcohol and 4+2+3=9 units water
or, 21 units alcohol in 30 units of mixture
21/30 *100 = 70%

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##### General Discussion
Intern
Joined: 22 Dec 2015
Posts: 39
Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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20 May 2016, 08:54
Concentration of Alcohol in 3 solutions are: 3/5, 4/5 and 7/10. Since equal parts are taken, let us assume 10 litres of each mixture was taken out. So,

Alcohol from Sol1 = 6
Alcohol from Sol2 = 8
Alcohol from Sol1 = 7

% of Alcohol in final solution = [(6 + 8 + 7)/30] * 100 = 70 %
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Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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20 May 2016, 09:52
VeritasPrepKarishma wrote:
Quote:
The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?
A)65%
B)70%
C)75%
D)80%

how can the following problem be solved using the scale/ratio formula method?

Solution:

With 3 quantities, the most straight forward method would be our usual weighted average formula.
We can use the scale method on two quantities at a time.
Here, I say that solution 1 has 3/5 alcohol and solution 2 has 4/5 alcohol. When we mix 1 part of each, we will get a mixture with 3.5/5 alcohol (it's simple average because both solutions are mixed in equal quantities).

3.5/5 = 7/10

Solution 3 has 7/10 alcohol.

2 parts of previous mix is mixed with 1 part of solution 3 but both have 7/10 alcohol. So the total mixture will have 7/10 = 70% alcohol.

ALTERNATE APPROACH

Let the composition of mixtures be -

A = Alcohol (30) Water (20) { RATIO IS 3:2}
B = Alcohol (40) Water (10) { RATIO IS 4:1}
C = Alcohol (35) Water (15) { RATIO IS 7:3}

Quote:
if equal quantities of the mixture are drawn and mixed

Let 10 units is drawn -

A = Alcohol (6) Water (4) { RATIO IS 3:2}
B = Alcohol (8) Water (2) { RATIO IS 4:1}
C = Alcohol (7) Water (3) { RATIO IS 7:3}

Total alcohol = 21 and water = 9

Net concentration of alcohol is 21/30*100 =>70%

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Abhishek....

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Manager
Joined: 27 Apr 2016
Posts: 93
Location: Brazil
GMAT 1: 610 Q37 V36
GPA: 2.7
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Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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20 May 2016, 12:13
1
You just have to sum the ratios, and then you'll have 14:6 which equals 7:3, so you have 7 parts alcohol for every 3 of water (70%).
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Status: It's near - I can see.
Joined: 13 Apr 2013
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Location: India
GMAT 1: 480 Q38 V22
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Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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05 Dec 2017, 22:40
VeritasPrepKarishma wrote:
Quote:
The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?
A)65%
B)70%
C)75%
D)80%

how can the following problem be solved using the scale/ratio formula method?

Solution:

With 3 quantities, the most straight forward method would be our usual weighted average formula.
We can use the scale method on two quantities at a time.
Here, I say that solution 1 has 3/5 alcohol and solution 2 has 4/5 alcohol. When we mix 1 part of each, we will get a mixture with 3.5/5 alcohol (it's simple average because both solutions are mixed in equal quantities).

3.5/5 = 7/10

Solution 3 has 7/10 alcohol.

2 parts of previous mix is mixed with 1 part of solution 3 but both have 7/10 alcohol. So the total mixture will have 7/10 = 70% alcohol.

I got it this way:

Alcohol : 3+4+7 = 14

Total solution : (3+2) + (4+1) + (7+3) = 5+5+10 = 20

Concentration of alcohol = 14*100/20 = 70%

Is the correct way? Please suggest.
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Intern
Joined: 07 May 2017
Posts: 22
Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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19 May 2018, 23:38
1
VeritasPrepKarishma wrote:
Quote:
The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be?
A)65%
B)70%
C)75%
D)80%

how can the following problem be solved using the scale/ratio formula method?

This is how i did it.

Most helpful tip in this question is that all the three mixtures are in equal quantities.
just add the alcohol parts and divide by the total parts.
i.e mixture 1 has 3 parts alcohol out of 5 parts solution
mixture 2 has 4 parts alcohol out of 5 parts solution.
mixture 3 has 7 parts alcohol out of 10 parts solution (can be written as 3.5 parts alcohol out of 5 parts solution)

alcohol=3+4+3.5=10.5 parts
total=15 parts
concentration= 10.5/15*100=70%

ANS = B. SIMPLE!

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Intern
Joined: 25 Feb 2018
Posts: 9
Re: The ratio of alcohol and water in three mixtures of alcohol and water  [#permalink]

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22 May 2018, 23:55
take 10parts each (given, equal amount)
For 3:2 => 6 parts alcohol and 4 parts water
For 4:1 l=> 8 parts alcohol and 2 parts water
for 7:3 => 10, 7 parts alcohol and 3 parts water.

Mixing these three will give 6+8+7 =21 units alcohol and 4+2+3=9 units water
or, 21 units alcohol in 30 units of mixture
21/30 *100 = 70%

Re: The ratio of alcohol and water in three mixtures of alcohol and water   [#permalink] 22 May 2018, 23:55
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