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12.5% of a solution having milk and water in the ratio 24 : 25 is remo

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12.5% of a solution having milk and water in the ratio 24 : 25 is remo  [#permalink]

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New post 27 Feb 2019, 10:56
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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
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Joined: 04 Aug 2010
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12.5% of a solution having milk and water in the ratio 24 : 25 is remo  [#permalink]

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New post 27 Feb 2019, 13:28
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cfc198 wrote:
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


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:
\(\frac{milk}{water} = \frac{21}{43}\)


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Re: 12.5% of a solution having milk and water in the ratio 24 : 25 is remo  [#permalink]

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New post 27 Feb 2019, 22:46
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cfc198 wrote:
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


We have discussed removal and replacement in detail here: https://www.veritasprep.com/blog/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)
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Re: 12.5% of a solution having milk and water in the ratio 24 : 25 is remo   [#permalink] 27 Feb 2019, 22:46
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