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27 Feb 2019, 10:56
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:39) correct
46%
(02:56)
wrong
based on 212
sessions
History
Date
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12.5% of a solution having milk and water in the ratio 24 : 25 is removed and replaced with water. Find the ratio of milk and water in the solution if this operation is done a total of three times.
1. 21 : 64
2. 27 : 64
3. 8 : 27
4. 27 : 33
5. 21 : 43
1. 21 : 64
2. 27 : 64
3. 8 : 27
4. 27 : 33
5. 21 : 43
27 Feb 2019, 13:28
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cfc198
12.5% of a solution having milk and water in the ratio 24 : 25 is removed and replaced with water. Find the ratio of milk and water in the solution if this operation is done a total of three times.
1. 21 : 64
2. 27 : 64
3. 8 : 27
4. 27 : 33
5. 21 : 43
1. 21 : 64
2. 27 : 64
3. 8 : 27
4. 27 : 33
5. 21 : 43
Since \(\frac{milk}{water} = \frac{24}{25}\), \(\frac{milk}{total}= \frac{24}{49}\)
Portion removed each time = 12.5% = \(\frac{1}{8}\)
Each time \(\frac{1}{8}\) of the total volume is removed, \(\frac{7}{8}\) of the milk remains in the container.
After the removal process is performed 3 times, we get:
\(\frac{milk}{total}= \frac{7}{8} * \frac{7}{8} * \frac{7}{8} * \frac{24}{49} = \frac{21}{64}\)
Of every 64 liters in the container, milk = 21 liters, with the result that water = 64-21 = 43 liters.
Thus:
\(\frac{milk}{water} = \frac{21}{43}\)
General Discussion
27 Feb 2019, 22:46
Kudos
Bookmarks
cfc198
12.5% of a solution having milk and water in the ratio 24 : 25 is removed and replaced with water. Find the ratio of milk and water in the solution if this operation is done a total of three times.
1. 21 : 64
2. 27 : 64
3. 8 : 27
4. 27 : 33
5. 21 : 43
1. 21 : 64
2. 27 : 64
3. 8 : 27
4. 27 : 33
5. 21 : 43
We have discussed removal and replacement in detail here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... -mixtures/
If 1/8th of the solution is removed and replaced with water, the quantity of milk after removal is the same as quantity of milk after adding water (since only water is added).
Concentration of milk (Ci) = 24/49
Since 1/8th of the solution is removed, Vi/Vf = 7/8
Since the process is repeated 3 times,
Cf = Ci *(Vi/Vf)^3
Cf = (24/49) * (7/8)^3 = 21/64
Ratio of milk:water = 21:43
Answer (E)
