Pipe A can fill a Tank in 30 min, while pipe B can fill

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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?

1. 9³/₁₃ h
2. 9⁴/₁₃ h
3. 9⁷/₁₃ h
4. 9⁹/₁₃ h

Correct Option: A

Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/10
Part emptied by C in 1 min = - 1/40
Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 )
= (4 + 12 - 3)/120 = 13/120

∴ Required time to fill the tank = 120/13 = 9³/₁₃ h