Pipe A can fill a tank in 30 min, while pipe B can 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, how much time will be needed to make the tank full?

A) \( \Large 9\frac{3}{13} \) h
B) \( \Large 9\frac{4}{13} \) h

C) \( \Large 9\frac{7}{13} \) h
D) \( \Large 9\frac{9}{13} \) h

Correct answer:
A) \( \Large 9\frac{3}{13} \) h

Description for Correct answer:
Part filled by A in 1 min = \( \Large \frac{1}{30} \)

Part filled by B in 1 min = \( \Large \frac{1}{10} \)

Part emptied by C in 1 min = \( \Large \frac{1}{40} \)

Net part filled in 1 h by (A + B + C)

= \( \Large \left(\frac{1}{30}+\frac{1}{10}-\frac{1}{40}\right) \)

= \( \Large \frac{4+12-3}{120} = \frac{13}{120} \)

Therefore, Required time to fill the tank = \( \Large \frac{120}{13} \)h = \( \Large 9\frac{3}{13} \) h

Please provide the error details in above question

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