| Pipe A can fill a tank in 30 min, while pipe B cam fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, then how much time will be needed to make the tank full? |
A) \[9\frac{3}{13}h\]
B) \[9\frac{4}{13}h\]
C) \[9\frac{7}{13}h\]
D) \[9\frac{9}{13}h\]
E) None of these
Correct Answer: A
Solution :
| Part filled by A in 1 min \[=\frac{1}{30}\] |
| Part filled by B in 1 min \[=\frac{1}{10}\] |
| Part emptied by the C in 1 min \[=-\frac{1}{40}\] |
| Net part filled in 1 h by (A + B + C) |
| \[=\left( \frac{1}{30}+\frac{1}{10}-\frac{1}{40} \right)=\frac{4+12-3}{120}=\frac{13}{120}\] |
| \[\therefore \]Required time to fill the tank \[=\frac{120}{13}=9\frac{3}{13}h\] |
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