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A certain quantity of 40% solution is replaced with 25% solu [#permalink]

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24 Dec 2003, 21:28

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A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

Ok Shabang, I'll try to explain this to you since it appears most people are away celebrating x-mas. Studying for the GMAT is how I'm celebrating X-mas this year.

I would pick numbers here and scan the answer choices (also think logically - the difference in the percentage of the solution declines by only 5% when added with the diluted solution - thus I would get rid of answer choices c,d,e - so I'm left with a and b) I chose b off the bat:

Pick 60 (ml, oz, whatever) as the total mixture - it works well with 3, 4, and 5.

You have a mixture that is 40% solution: 2:5=x:60 thus x = 24 solution : 60 total mixture

Using answer choice B 1/3 - plug it in. 1/3 of 60 is 20 so you're left with 40 oz of the solution. Thus the new solution is 2:5=x:40 x=16 solution: 40 total mixture. You're adding 20 oz of a diluted mixture. thus 1/4 = x/20 = 5 solution: 20 total mixture. Add them together you have: 21 solution : 60 total mixture or 21/60 = 35%.

I'm a little buzzed - I hoep ti amkes sense.

Last edited by Titleist on 25 Dec 2003, 17:04, edited 1 time in total.

Indeed, not easy to explain with words. My explanation is:

Let's say that the total original mixture A is 100ml

The original mixture A thus has 40ml of alcohol out of 100ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25ml of alcohol per 100ml. Thus, the difference between 40ml and 25ml is 15ml per 100ml of mixture. This means that everytime you replace 100ml of the original mixture A by 100ml of mixture B, the original alcohol concentration will decrease by 15%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 5%. Therefore, 5 out of 15 is 1/3 and B is the answer. Was that clear?[/b]

Initial solution = x
concentration of solvent = .4x

Lets remove 'y' from the total solution
Solvent in the removed solution = .4y

We add back 'y' into the solution
Solvent in the added solution = .25y
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Adding,
Total solution = x-y+y = x
Solvent = .4x - .4y + .25y = .4x - .15y

In this kinds of problems, we should always try to apply the concept of weighted average.

(strength of one solution) (quantity of that solution) + (strength of another solution) (quantity of that solution) = (strength of resultant solution) (quantity of the resultant solution)

This is how I did it. But it took some time for me to come up with a solution.

I like beer so I will go with this example.
The beer contained 40% alcohol 60% water. from this x amount was taken out. This x amount will carry same amount of alcohol with it so we have

A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

oringal quantity of solution=1 solution replaced = x

0.4 *(1-x)+0.25x= 0.35 *1

0.05= 0.15 x--> x= 1/3
_________________

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I back solved it: Since it deals with percent, lets take 100 as the base.

When 1/4 - total mixrure is 40 + 25*4 / 500 = 140/500 ; this is not eq 35. When 1/3 - total mixture is 40 + 25*3/ 400 = 115/400 = 35% - this is the ans. When 1/2 - total mixture is 40 + 20*2/ 300 = 80/300 ; not eq 35% Similarly for D & E.

i belive here 1-x is the remaining soln. Now can you why are we taking 40 % of 1-x. I do not get it. Appreciate ur help.

0.4 *(1-x)+0.25x= 0.35 *1

Let me try out, the logic here is

You removed x quantity of 40% concentration solution from 1 and added same x quantity of 25% concentration solution, which total to original quantity 1 of solution with 35% concentration. Hence

Remaining quantity of 40% solution + added quantity of 25% solution = Total solution with 35% concentration. 0.4(1-x) + 0.25x = .35

A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

Let actual solution be "T" Replaced solution be "R"

A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

Or use our standard mixtures formula for replacements too. In a certain quantity of 40% solution, 25% solution is added to give 35% solution. w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 35)/(35 - 25) = 1/2 So quantity of 40% sol:25% solution = 2:1 This means the initial total solution was 3 and the fraction of 25% now in the mixture is 1. Therefore, 1/3 of the 40% solution was removed and replaced with 25% solution.

Re: A certain quantity of 40% solution is replaced with 25% [#permalink]

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30 May 2014, 12:34

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A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) 3/4

Or use our standard mixtures formula for replacements too. In a certain quantity of 40% solution, 25% solution is added to give 35% solution. w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 35)/(35 - 25) = 1/2 So quantity of 40% sol:25% solution = 2:1 This means the initial total solution was 3 and the fraction of 25% now in the mixture is 1. Therefore, 1/3 of the 40% solution was removed and replaced with 25% solution.

However I do not really understand the last part where you say that 1/3 of the original solution was replaced. Do you get to 3 by adding 2 and 1?

And why is 40% 1/3 of the original solution?

I also tried to solve it using smart numbers but did not work...

From your calculations, you get that when you mix 2 parts of 40% solution with 1 part of 25% solution, you get resultant 35% solution.

Initially, you had only 40% solution. You removed say x of it and put x of 25% solution in its place. This x was 1 part and you had 2 parts of 40% solution left. So initially, you must have had 3 parts of 40% solution. You then must have removed 1 part and replaced it with 25% solution. That is how you would have ended up mixing 2 parts of 40% with 1 part of 25% to get 35% solution.

So we must have replaced 1 part out of 3 (i.e. 1/3) of the original 40% solution.
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