| Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill? [SSC (CGL) 2013, (CPO) 2010 |
A) \[8\frac{1}{4}\,\,\min \]
B) \[8\frac{3}{4}\,\,\min \]
C) \[5\,\,\min \]
D) \[8\frac{1}{2}\,\,\min \]
Correct Answer: A
Solution :
| Given, time taken by P to fill the tank =12 min |
| and time taken by Q to fill the tank = 15 min |
| Then, pan filled by both pipes in 1 min |
| \[=\frac{1}{12}+\frac{1}{15}=\frac{5+4}{60}=\frac{9}{60}\] |
| Now, part filled in 3 min \[=\frac{3\times 9}{60}=\frac{27}{60}=\frac{9}{20}\] |
| \[\therefore \]Remaining part \[=1-\frac{9}{20}=\frac{11}{20}\] |
| Now, the remaining part is filled by pipe Q in x min. |
| \[\therefore \]Remaining time = Remaining part \[\times \] Q's time |
| \[\Rightarrow \] \[x=\frac{11}{20}\times 15=\frac{11\times 3}{4}=\frac{33}{4}=8\frac{1}{4}\min \] |
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