A container holds 4 quarts of alcohol and 4 quarts of water. How many

Question

A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?

A. 4/3
B. 5/3
C. 7/3
D. 8/3
E. 10/3

ENGRTOMBA2018 · Accepted Answer

An alternate to the alligation method is the more direct/algebraic method:

Let x be the amount of water to be added.

New total amount of water = 4+x

Total amount of alcohol = 4

New total = 4+4+x=8+x

Final ratio required (for water) = 5/(5+3)=5/8

Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.

D is thus the correct answer.

Hope this helps.

sudhir18n · Answer

Currently its is 4 units of Alcohol and 4 units of water
to make the ratio 3/5 ; how much water has to be added?

4/4+x =3/5
20 = 12+3x
x= 8/3
Its D

subhashghosh · Answer

Let the number of quarts that should be added to get the required ratio = x

So total quarts of water = (x + 4)

But the original number of quarts of alcohol remains the same, so we have :

4/(x+4) = 3/5

Cross-multiply:

Now we have 20 = 3x + 12

=> 3x = 20 -12

=> x = 8/3

Answer - D

sameerkamath21 · Answer

VeritasPrepKarishma

Hello Karishma. I recently read your blog posts on weighted averages and found the w1/w2 method and the scale method to be very useful, fast and accurate. So i've just started solving mixture problems using your techniques as much as possible. Will take sometime for me to master it. Could you please explain the how you can solve this sum using your method? Thanks

KarishmaB · Answer

Right now the concentration of water in the mix is 4/8. We want to add pure water (8/8) to it and make the concentration of water in the final solution (5/8).

w1/w2 = (8/8 - 5/8)/(5/8 - 4/8) = 3/1

So for every 3 parts of the original mix, we should add 1 part of pure water. 
The original mix is 8 quarts. So we should add 8/3 quarts of pure water.

Answer (D)

sameerkamath21 · Answer

VeritasPrepKarishma

Thank you so much Karishma. Just one doubt. The A2 and A1 that you used in your blog post about the same topic keep changing as per the question right? And what will w1/w2 be in this case?As in acc to this question?

KarishmaB · Answer

I am not sure I understand what your question is. Do you mean to ask how we decide on how to allocate subscripts? This post shows one way: https://gmatclub.com/forum/a-container- ... l#p1935591 Alternatively, pure water can be A1, w1 and the 50-50 mix can be A2, w2. The answer obtained will be the same. Again, you worked with concentration of water here. You could work with the concentration of alcohol too (pure water having 0 alcohol).

dave13 · Answer

Hi VeritasPrepKarishma , thanks for the link you shared in the previous post https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2017/1 ... -averages/ that confusion regarding nnomenclature is clear

now after reading the explanation which is followed by an example i have a question: regarding this : w1/w2 = (8/8 - 5/8)/(5/8 - 4/8) = 3/1 where does it say that we need to add 8/8 pure water, it says 3 parts of alcohol and only 5 parts of water and not 8

please explain

Now another question, when you get this 3/1 you say " So for every 3 parts of the original mix, we should add 1 part of pure water. The original mix is 8 quarts. So we should add 8/3 quarts of pure water. " let me break it down: "So for every 3 parts of the original mix" doesn't "3" in numerator refer to water?

"we should add 1 part of pure water" doesn`t "1" in denominator refer to alcohol ?

thank you:-)

KarishmaB · Answer

Note that 8/8 is the concentration of water in water i.e. the water is fully water only and hence its concentration is 1. How many parts is the weight, not the concentration.
The concentration of water in the mix is 4/8 and final concentration of water is 5/8 so to ease our calculations, we write 1 as 8/8 (= 1). 
The concentration of an ingredient (C1, C2 and Cavg) is expressed as Ingredient/Total (not Ingredient1/Ingredient2).

w1 and w2 are the weights of total solution (including both ingredients) in the two cases
w1/w2 = 3/1 
So for every 3 parts of mix (water + alcohol), we put 1 part of water (pure water). When we do this, we will get water concentration of 5/8.

ScottTargetTestPrep · Answer

We can create the equation in which w = the number of quarts of water added:

4/(4+w) = 3/5

20 = 12 + 3w

8 = 3w

8/3 = w

Answer: D

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A container holds 4 quarts of alcohol and 4 quarts of water. How many

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