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 Author: Bunuel [ 12 Nov 2021, 05:15 ] Post subject: 15 liters are taken of from a container full of liquid A and replaced 15 liters are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more liters of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16, what is the capacity of the container?A. 45E. 42C. 37.5D. 36B. 25

 Author: RanonBanerjee [ 14 Nov 2021, 11:15 ] Post subject: Re: 15 liters are taken of from a container full of liquid A and replaced Answer choice C.Final volume of of A is 9x/25 given x is the capacity of the container, i.e, the volume of A to begin with.From the equation of multiple replacements,9x/25= x(1-15/x)^29/25= (1-15/x)^2(3/5)^2 = (1-15/x)^23/5 = 1-15/xX=75/2 =37.5Posted from my mobile device

 Author: GMATGuruNY [ 14 Nov 2021, 15:29 ] Post subject: 15 liters are taken of from a container full of liquid A and replaced Bunuel wrote:15 liters are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more liters of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16, what is the capacity of the container?A. 45E. 42C. 37.5D. 36B. 25After two replacements, the resulting ratio of A to B -- $$\frac{9}{16}$$ -- indicates that A constitutes $$\frac{9}{25}$$ of the resulting solution.Implication:After each replacement, $$\frac{3}{5}$$ of A remains in the container, with the result that -- after two replacements -- the remaining amount of A = $$\frac{3}{5}*\frac{3}{5}=\frac{9}{25}$$.Since 3/5 of A remains after the first replacement -- implying the removal of 2/5 of A -- the 15-liter reduction in A must constitute 2/5 of the total volume of A in the full container:$$15 = \frac{2}{5}x$$$$75 = 2x$$$$x = 37.5$$

 Author: Vibhatu [ 13 Jan 2023, 00:50 ] Post subject: Re: 15 liters are taken of from a container full of liquid A and replaced Bunuel please post the official solution with details.

 Author: Kinshook [ 13 Jan 2023, 01:26 ] Post subject: Re: 15 liters are taken of from a container full of liquid A and replaced Given: 15 liters are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more liters of the mixture is taken and replaced with liquid B. Asked: After this process, if the container contains Liquid A and B in the ratio 9:16, what is the capacity of the container?Let the capacity of the container be VFirst ReplacementLiquid A = V-15Liquid B = 15Total = VLiquid A/Total = (V-15)/VLiquid B/Total = 15/VSecond replacementLiquid A = V-15 - 15(V-15)/V = (V-15)(1-15/V) = (V-15)ˆ2/VLiquid B = V - (V-15)ˆ2/V = {Vˆ2 - (V-15)ˆ2}/VRatio Liquid A and Liquid B = (V-15)ˆ2 / {Vˆ2 - (V-15)ˆ2} = 9/16(V-15)ˆ2/Vˆ2 = 9/25(V-15)/V = 3/5V/15 = 5/2V = 75/2 = 37.5IMO C

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