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.

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)
_________________

Thanks and Regards

Abhishek....

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