| Two pipes A and B can fill a cistern in \[37\frac{1}{2}\min \] min and 45 min respectively. Both pipes are opened. The cistern will be filled just in half an hour, if the pipe B is turned off after |
A) 15 min
B) 10 min
C) 5 min
D) 9 min
Correct Answer: D
Solution :
| Pipe A fills the tank in \[\frac{75}{2}\,\,\min .\] |
| \[\therefore \] Part of the tank filled by A in 30 min |
| \[=\frac{2}{75}\times 30=\frac{4}{5}\] |
| Remaining part \[=1-\frac{4}{5}=\frac{1}{5}\] |
| Now, 1 part is filled by pipe B in 45 min. |
| \[\therefore \] \[\frac{1}{5}\]part is filled in \[45\times \frac{1}{5}=9\,\min \] |
| Hence, the pipe B should be turned off after 9 min. |
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