| Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. Both are opened together but at the end of 3 min, P is turned off. In how many more minutes will Q fill the cistern? [SSC (CPO) 2010] |
A) 7 min
B) \[7\frac{1}{2}\,\,\min \]
C) 8 min
D) \[8\frac{1}{4}\,\,\min \]
Correct Answer: D
Solution :
| 1 min work of \[P=\frac{1}{12}\]\[\Rightarrow \]1min work of \[Q=\frac{1}{15}\] |
| 1 min work of P and Q both \[=\frac{1}{12}+\frac{1}{15}=\frac{3}{20}\] |
| \[\Rightarrow \] 3 min work of P and \[Q=\frac{9}{20}\] |
| \[\therefore \] Remaining work \[=1-\frac{9}{20}=\frac{11}{20}\] |
| Time taken by \[Q=\frac{11}{20}\times 15=\frac{33}{4}=8\frac{1}{4}\min \] |
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