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12 Nov 2021, 05:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (02:29) correct
39%
(02:46)
wrong
based on 210
sessions
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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
A. 45
E. 42
C. 37.5
D. 36
B. 25
14 Nov 2021, 15:29
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Bunuel
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:
\(15 = \frac{2}{5}x\)
\(75 = 2x\)
\(x = 37.5\)
General Discussion
RanonBanerjee
Joined: 04 Dec 2020
Last visit: 11 Mar 2025
Posts: 35
Given Kudos: 153
Concentration: Technology, Strategy
Schools: Fuqua '27 (S)
14 Nov 2021, 11:15
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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
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
