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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. 45 E. 42 C. 37.5 D. 36 B. 25 |
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| 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)^2 9/25= (1-15/x)^2 (3/5)^2 = (1-15/x)^2 3/5 = 1-15/x X=75/2 =37.5 Posted from my mobile device |
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| 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. 45 E. 42 C. 37.5 D. 36 B. 25 After 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: \(15 = \frac{2}{5}x\) \(75 = 2x\) \(x = 37.5\) |
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| 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. |
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| 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 V First Replacement Liquid A = V-15 Liquid B = 15 Total = V Liquid A/Total = (V-15)/V Liquid B/Total = 15/V Second replacement Liquid A = V-15 - 15(V-15)/V = (V-15)(1-15/V) = (V-15)ˆ2/V Liquid B = V - (V-15)ˆ2/V = {Vˆ2 - (V-15)ˆ2}/V Ratio Liquid A and Liquid B = (V-15)ˆ2 / {Vˆ2 - (V-15)ˆ2} = 9/16 (V-15)ˆ2/Vˆ2 = 9/25 (V-15)/V = 3/5 V/15 = 5/2 V = 75/2 = 37.5 IMO C |
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