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

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The ratio of alcohol and water in three mixtures of alcohol and water [#permalink]

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New post 15 Feb 2016, 21:28
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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%

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


Solution:

[Reveal] Spoiler:
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.

Answer (B)
[Reveal] Spoiler: OA

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Re: The ratio of alcohol and water in three mixtures of alcohol and water [#permalink]

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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%

Answer : B
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Re: The ratio of alcohol and water in three mixtures of alcohol and water [#permalink]

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New post 20 May 2016, 09:54
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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New post 20 May 2016, 10:52
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:

[Reveal] Spoiler:
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.

Answer (B)



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%

Answer will be (B)
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Re: The ratio of alcohol and water in three mixtures of alcohol and water [#permalink]

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New post 20 May 2016, 13:13
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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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Re: The ratio of alcohol and water in three mixtures of alcohol and water [#permalink]

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New post 05 Dec 2017, 23:40
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:

[Reveal] Spoiler:
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.

Answer (B)


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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Re: The ratio of alcohol and water in three mixtures of alcohol and water   [#permalink] 05 Dec 2017, 23:40
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