A solution that is 20% acetic acid by volume is mixed with a

Question

A solution that is 20% acetic acid by volume is mixed with a solution that is 50% acetic acid by volume , resulting in a mixture that is 40% acetic acid by volume .
This 40% solution is then mixed with a solution that is 10% acetic acid by volume , resulting in a solution that is 20% acetic acid by volume . What is the ratio of the volume of the 50% solution of acetic acid to the volume volume of the 10% solution of acetic acid ?

A) 1:3
B) 1:2
C) 1:1
D) 2:1
E) 3:1

A) 1:3
B) 1:2
C) 1:1
D) 2:1
E) 3:1

freedom128 · Accepted Answer

Hi  LeenaSai

Let define as follows: 
Volume of solution that is 20% acetic acid = a
Volume of solution that is 50% acetic acid = b
Volume of solution that is 10% acetic acid = c

A solution that is 20% acetic acid by volume is mixed with a solution that is 50% acetic acid by volume , resulting in a mixture that is 40% acetic acid by volume. 
=> (0.2a+0.5b) / (a+b) = 0.4
=> 0.2a+0.5b = 0.4 (a+b) 
=> 0.1b = 0.2a
=> b = 2a

This 40% solution is then mixed with a solution that is 10% acetic acid by volume , resulting in a solution that is 20% acetic acid by volume. 
=> (0.2a+0.5b+0.1c) / (a+b+c) = 0.2
=> 0.2a +0.5b +0.1c = 0.2a +0.2b +0.2c
=> 0.5b + 0.1c = 0.2b + 0.2c
=> 0.3b = 0.1c
=> 3b = c
=> b:c = 1:3

(A) is the answer

LeenaSai · Answer

I am getting the answer 1:1 which is wrong !!
Can anyone help ,

Posted from my mobile device

LeenaSai · Answer

I coulnt understand the comment our part of your explanation, can you please clarify

ChauhanR · Answer

The key to these problems is that the combined total of the concentrations in the two parts must be the same as the whole mixture.

Assume, Volume of 1st mixture = x
Volume of 2nd mixture = y
Volume of 3rd mixture = z

We have to find, y/z=?

Therefore,
20x + 50y = 40(x+y) , which gives y=x/2.

Now mix of 1st & 2nd is mixed with 3rd,
40(x+y) + 10z = 20 (x+y+z)

On Solving, we will get y/z=1/3

Ans. A

Hope it helps.

Posted from my mobile device

LeenaSai · Answer

Hi ChauhanR ,

Now it’s pretty clear ?

LeenaSai · Answer

Thanks Chondro for the explanation ?

ScottTargetTestPrep · Answer

Solution:
 
Let A be the volume of the 20% solution, B be the volume of the 50% solution and C be the volume of the 10% solution. We need to determine the ratio B/C.

We are told that mixing the 20% solution with the 50% solution results in a solution that has a concentration of 40%. The volume of acetic acid in the 20% and 50% solutions are 0.2A and 0.5B, respectively. Thus, we can create the following equation:

(0.2A + 0.5B)/(A + B) = 40/100

(0.2A + 0.5B)/(A + B) = 4/10

2A + 5B = 4A + 4B

B = 2A

Next, we are told that the resulting 40% solution is mixed with the 10% solution that has a volume of C. Notice that the volume of the 40% solution is A + B = A + 2A = 3A. Further, the amount of acetic acid in the 40% and the 10% solutions are 0.4(3A) = 1.2A and 0.1C, respectively. Thus:

(1.2A + 0.1C)/(3A + C) = 20/100

(1.2A + 0.1C)/(3A + C) = 2/10

12A + C = 6A + 2C

6A = C

Hence, the ratio of the volume of the 50% solution to the volume of the 10% solution is B/C = 2A/6A = 1/3.

Answer: A

rsrighosh · Answer

I tried to use weighted average technique

Let A:20% acetic acid; B: 50% Acetic Acid; resultant C: 40% Acetic Acid

\frac{A}{B} = \frac{50-40}{40-20} = \frac{1}{2}

So, ideally C is A+B which makes C as 1+2 = 3

Now let D: 10% Acetic acid; resultant E: 20% Acetic Acid

So, 
 \frac{C}{D} = \frac{10-20}{20-40} = \frac{1}{2}

OR  \frac{3}{D} = \frac{1}{2}

OR D = 6

hence, A is 1 part, B is 2 parts, C is 3 parts and D is 6 parts

Hence  \frac{B}{D} =\frac{ 2}{6} = \frac{1}{3}

VeritasKarishma  is this approach correctly put?

KarishmaB · Answer

Yes, absolutely! As next step, try to do all this in your mind. e.g. avg 40% is 2:1 away from 20% and 50%. Then 20% and 50% are taken in reverse ratio 1:2 (20% and 50% respectively).
Avg 20% is 2:1 away from 40% and 10% so they are taken in the ratio 1: 2 which is 3:6. 
So 2 parts of 50% and 6 parts of 10% which gives us 1:3.

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A solution that is 20% acetic acid by volume is mixed with a

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