| A 20 L mixture contains milk and water in the respective ratio of 3: 2. If 10 L of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removals and replacement, then what is the ratio of milk and water in the resultant mixture respectively? |
A) 17: 3
B) 9: 1
C) 4: 17
D) 5: 3
E) 3: 14
Correct Answer: B
Solution :
| Total mixture \[=20\,\,L\] |
| Ratio of milk and water \[=3:2\] |
| \[\therefore \]Quantity of milk \[=20\times \frac{3}{5}=12\,\,L\] |
| Quantity of water \[=20\times \frac{2}{5}=8\,\,L\] |
| When 10 L of mixture is removed, then milk removed |
| \[=10\times \frac{3}{5}=6\,\,L\] |
| and water removed \[=4\,\,L\] |
| Now, ratio \[=\frac{12-6+10}{8-4}=\frac{16}{4}=\frac{4}{1}\] |
| Again, from this mixture 10 L is removed |
| Milk removed \[=\frac{4}{5}\times 10=8\,\,L\] |
| and water removed \[=\frac{1}{5}\times 10=2\,\,L\] |
| Hence, required ratio \[\frac{16-8+10}{4-2}=\frac{18}{2}=\frac{9}{1}=9:1\] |
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