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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41% (02:16) correct 
