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

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Senior Manager
Joined: 29 Nov 2018
Posts: 280
Concentration: Marketing, Strategy
12.5% of a solution having milk and water in the ratio 24 : 25 is remo  [#permalink]

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27 Feb 2019, 10:56
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47% (02:10) correct 53% (03:03) wrong based on 34 sessions

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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
Senior Manager
Joined: 04 Aug 2010
Posts: 477
Schools: Dartmouth College
12.5% of a solution having milk and water in the ratio 24 : 25 is remo  [#permalink]

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27 Feb 2019, 13:28
4
1
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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##### General Discussion
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: 12.5% of a solution having milk and water in the ratio 24 : 25 is remo  [#permalink]

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27 Feb 2019, 22:46
1
1
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

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Karishma
Veritas Prep GMAT Instructor

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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