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VeritasPrepKarishma
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.

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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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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VeritasPrepKarishma
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.

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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VeritasPrepKarishma
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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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%

Answer : B
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