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# Eight litres are drawn off from a vessel full of water and s

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Joined: 13 Jul 2015
Posts: 57
Location: Singapore
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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02 Oct 2015, 03:04
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?
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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?
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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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06 May 2017, 05:22
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
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Joined: 14 May 2015
Posts: 52
Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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06 May 2017, 09:32
9x/49 = x((x-8)/x)^2
5x^2 - 98x + 392
x=14
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Joined: 17 Dec 2012
Posts: 637
Location: India
Eight litres are drawn off from a vessel full of water and s  [#permalink]

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10 Jun 2017, 03:07
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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Re: Eight litres are drawn off from a vessel full of water and s  [#permalink]

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29 Jun 2018, 01:58
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Re: Eight litres are drawn off from a vessel full of water and s &nbs [#permalink] 29 Jun 2018, 01:58

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