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g106
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A 48 lts container containing liquid A and B contains 25% liquid A. 29 Sep 2011, 12:43
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95% (hard)

Question Stats:

40% (02:23) correct 60% (03:02) wrong based on 158 sessions

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A 48 lts container containing liquid A and B contains 25% liquid A. a few lts of the mixture is released and replaced with equal amount of Liquid B. If this process is repeated once, the cylinder is found to contain 16% liquid A .How many lts of the mixture was released each time.?


A)4.8
B)9.6
C)7.68
D)9
E)None of the Above
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B
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A 48 lts container containing liquid A and B contains 25% liquid A. 28 Oct 2014, 19:51
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We need to use formula: New concentration = Initial concentration * (1 - replaced volume/total volume) exp Number of replacement.

Final concentration of liquid A = 0.16. Start concentration = 0.25 Number of replacement = 2
0.16 = 0.25 * (1 - X) exp 2

(1 - X) exp 2 = 64/100
1 - X = 4/5

so X = 1/5 (replaced volume/total volume)

1/5 * 48 lts = 9.6 lts
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A 48 lts container containing liquid A and B contains 25% liquid A. 01 Oct 2011, 03:07
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are you sure that this question is correct?
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A 48 lts container containing liquid A and B contains 25% liquid A. 01 Oct 2011, 08:53
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I tried to solve this, but the final quadratic equation has the negative discriminant and therefore it has no real roots. I suppose there should be a typo in the problem. I think there is no need to show the whole solution since calcuation are rather tough.
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A 48 lts container containing liquid A and B contains 25% liquid A. 01 Oct 2011, 16:27
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What is the source of this problem?
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A 48 lts container containing liquid A and B contains 25% liquid A. 02 Oct 2011, 02:56
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I solved it this way..But couldn't get any of the answers posted.

25% of mixture is liquid A => 12 ltrs of liquid A and 36 ltrs of liquid B together form 48 ltrs of the mixture.

This implies that the ratio of liquids A and B in the mixture is is 1:3

Let the amount of liquid removed i x ltrs => x/4 ltrs of liquid A and 3x/4 ltrs of liquid B is removed.

Given that the x liters of mixture removed is added with same quantity of liquid B =>

12-(x/4) + {36-(3x/4) + x} = 48
=> {12 -(x/4)} + {36 + x/4} = 48

The ratio of liquid A to total mixture after first time the process is done = 16% =>

{12- (x/4)} / 48 = 16/100

12- (x/4) = 7.68

x/4 = 4.32 => x= 17.28
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A 48 lts container containing liquid A and B contains 25% liquid A. 01 Apr 2016, 01:58
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g106
A 48 lts container containing liquid A and B contains 25% liquid A. a few lts of the mixture is released and replaced with equal amount of Liquid B. If this process is repeated once, the cylinder is found to contain 16% liquid A .How many lts of the mixture was released each time.?


A)4.8
B)9.6
C)7.68
D)9
E)None of the Above
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Responding to a pm:

The concept of replacement is discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/01 ... -mixtures/

Say x lts is released and replaced. We work with the element that doesn't change. So liquid A here.

\(Cfinal = Cinitial * \frac{(Vinitial)^n}{(Vfinal)^n}\)

\(.16 = .25 * \frac{(48 - x)^2}{48^2}\)


\(\frac{(48 - x)^2}{48^2} = \frac{16}{25} = \frac{4^2}{5^2}\)

\(x = 9.6 lts\)

Answer (B)
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