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11 Jan 2020, 06:40
Kudos
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D
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Difficulty:
95%
(hard)
Question Stats:
54% (02:47) correct
46%
(03:15)
wrong
based on 278
sessions
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From a solution containing milk and water in the ratio 2 : 3, 15 litres of solution is removed and replaced with 15 litres of milk. This operation is done once more. Now the ratio of milk to water is 7 : 5. What was the volume of the initial solution?
A. 60 litres
B. 70 litres
C. 80 litres
D. 90 litres
E. 100 litres
A. 60 litres
B. 70 litres
C. 80 litres
D. 90 litres
E. 100 litres
14 Jan 2020, 04:46
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yashwardhan
The logic of the method is discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... -mixtures/
The formula for multiple replacements is:
\(C2 = C1 * (V1/V2)^n\)
(5/12) = (3/5)*[(V - 15)/V]^2
(V - 15)/V = 5/6
V = 90
Answer (D)
23 Jul 2020, 19:13
Kudos
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When doing Iterations, we use the equation \(\frac{Final }{ Initial}\) = \((1 - \frac{b }{ a})^n\)
Final = The Final amount / Ratio of that substance who's concentration is being reduced.
Initial = The Initial amount / Ratio of that substance who's concentration is being reduced.
b = Amount of liquid (who's concentration is increasing) is added back
a = Final Volume in the container after the replacement of amount b.
n = number of iterations, or the number of times the process is repeated.
In the question Above
Let x L be the initial Volume of solution
Here the concentration of water is reducing and that of milk is increasing
Final Ratio = (5/12) * x
Initial Ratio = (3/5) * x
b = 15
a = x (as 15L are removed and replaced, the volume is unchanged)
n = 2
Substituting in the equation, \(\frac{Final }{ Initial}\) = \((1 - \frac{b }{ a})^n\)
\(\frac{(5/12)x}{(3/5)x}\) = \((1 - \frac{15 }{ x})^2\)
\(\frac{25}{36}\) = \((1 - \frac{15 }{ x})^2\)
Taking square root on both sides
\(\frac{5}{6}\) = \((1 - \frac{15 }{ x})\)
\(\frac{15}{x}\) = 1 - \(\frac{5}{6}\) = \(\frac{1}{6}\)
x = 15 * 6 = 90 L
Option D
Arun Kumar
Final = The Final amount / Ratio of that substance who's concentration is being reduced.
Initial = The Initial amount / Ratio of that substance who's concentration is being reduced.
b = Amount of liquid (who's concentration is increasing) is added back
a = Final Volume in the container after the replacement of amount b.
n = number of iterations, or the number of times the process is repeated.
In the question Above
Let x L be the initial Volume of solution
Here the concentration of water is reducing and that of milk is increasing
Final Ratio = (5/12) * x
Initial Ratio = (3/5) * x
b = 15
a = x (as 15L are removed and replaced, the volume is unchanged)
n = 2
Substituting in the equation, \(\frac{Final }{ Initial}\) = \((1 - \frac{b }{ a})^n\)
\(\frac{(5/12)x}{(3/5)x}\) = \((1 - \frac{15 }{ x})^2\)
\(\frac{25}{36}\) = \((1 - \frac{15 }{ x})^2\)
Taking square root on both sides
\(\frac{5}{6}\) = \((1 - \frac{15 }{ x})\)
\(\frac{15}{x}\) = 1 - \(\frac{5}{6}\) = \(\frac{1}{6}\)
x = 15 * 6 = 90 L
Option D
Arun Kumar
