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Current Student B
Joined: 12 Jul 2015
Posts: 84
Location: Singapore
Schools: LBS '21 (M)
GMAT 1: 730 Q50 V39 WE: Operations (Investment Banking)
Eight litres are drawn off from a vessel full of water and s  [#permalink]

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Bunuel wrote:
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk.If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters

Let the capacity of the vessel be $$x$$.

After the first removal there would be $$x-8$$ liters of water left in the vessel. Note that the share of the water would be $$\frac{x-8}{x}$$;

After the second removal, the removed mixture of 8 liters will contain $$8*\frac{x-8}{x}$$ liters of water, so there will be $$(x-8)-8*\frac{x-8}{x}=\frac{(x-8)^2}{x}$$ liters of water left.

As the ratio of water to milk after that is $$\frac{9}{40}$$, then the ratio of water to the capacity of the vessel would be $$\frac{9}{40+9}=\frac{9}{49}$$.

So $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

Bunuel, I understood your solution and I tried to work with milk too. what am I doing wrong?

1st pass: concentration of milk in solution: $$\frac{8}{x}$$

Removed: 8 litres of mixture --> 8 X $$\frac{8}{x}$$

Milk left: x - (8 X $$\frac{8}{x}$$) + 8 = $$\frac{x^2+8x-64}{x}$$

$$\frac{Milk}{Capacity}$$ = $$\frac{x^2+8x-64}{x^2}$$ = $$\frac{40}{49}$$

What am I doing wrong?
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------

update: bolded working should be Milk left: 8 - (8 X $$\frac{8}{x}$$) + 8 = $$\frac{16x-64}{x}$$

but that would lead to a very ugly quadratic equation: 10$$x^2$$ - 196x + 784 = 0 --> which gives the answer x =14

so my question is, is there anything in the question that prompted you to use water instead?
Director  V
Joined: 05 Mar 2015
Posts: 936
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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guerrero25 wrote:
VeritasPrepKarishma wrote:
nonameee wrote:
Bunuel, thanks a lot. I must have made some miscalculation.

Conceptually the question is interesting. However the numbers are quite "difficult" to work with. Do you think that a real GMAT question would have better numbers?

Actually, the numbers are quite suitable for a very efficient, quick and oral solution. This is what I thought of when I came up with the answer in 20 secs. Mind you, you need to go through the link provided below to understand this theory. Else the 20 sec solution will probably not make sense to you.

We are substituting milk so we should work with water.

Final concentration of water = 9/49
There were two iterations. So, 9/49 = (100%)*(Vi/Vf)^2
Vi/Vf = 3/7
Since we are putting 8 liters of water but difference between Vi and Vf is 4, final volume (which is also equal to volume of the vessel) must be twice too i.e. 7*2 = 14 liters.

http://www.veritasprep.com/blog/2012/01 ... -mixtures/

Hi Karishma , Could you please elaborate the highlighted portion ? I am unable to grasp the last part of the solution . Thanks in advance .

For the ease of understanding just consider initial volume be X then final required volume will be X+8
i.e Vi=X and Vf=X+8
now substitute this to equation (Vi/Vf)^2=9/49
u will get Vi=6
means Vf=6+8=14lts..Ans.
Intern  B
Joined: 29 Apr 2017
Posts: 16
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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Hello
I am solving this que as follows:

Assume the capacity of vessel is 20l

So after first withdrawal,
Water= 12l
Milk= 8l

After second withdrawal,
Water = 20 - 12/20*8 = 12.8l
Milk = 20 - 12.8 = 7.2l

Now this ratio is equal to 9/40

Thanks

Sent from my SM-N9200 using GMAT Club Forum mobile app
Intern  B
Joined: 14 May 2015
Posts: 45
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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9x/49 = x((x-8)/x)^2
5x^2 - 98x + 392
x=14
Director  S
Joined: 17 Dec 2012
Posts: 629
Location: India
Eight litres are drawn off from a vessel full of water and s  [#permalink]

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virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight liters of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters

1. We know a total of 16 L milk were added. Choice C which is 20 L capacity, implies that finally, at least 4L of water in excess was there after drawing .
2. So water is (4+x) and we know the milk added was 16L giving a ratio of (4+x)/16 which is greater than 9/40. On same reasoning all choices except D can be ruled out.
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Srinivasan Vaidyaraman
Magical Logicians
Holistic and Holy Approach
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Concentration: Entrepreneurship, Social Entrepreneurship
GMAT 1: 710 Q48 V42
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Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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Now again 8 liters of mixture is removes , so water in that mixture is w = (x-8/x) * 8
Non-Human User Joined: 09 Sep 2013
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Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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_________________ Re: Eight litres are drawn off from a vessel full of water and s   [#permalink] 01 Nov 2019, 09:26

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