2 pipes A & B can fill a cistern in 12 min and 16 min resp. If both pipes are opend together then after hw mch time B shld be closed so tht the tank is full in 9 min
Pipe A fills the tank in 12 minutes. In a minute 1/12 of the tank is filled. Similarly for tank B, in a minute 1/16 of the tank is filled.
When both the pipes are opened to fill the tank, let the time for which the pipe B is closed to fill the tank in 9 minutes be T.
This gives 9*(1/12) + (9 - T)*(1/16) = 1
=> 9/12 + 9/16 - T/16 = 1
=> T/16 = 9/12 + 9/16 - 1
=> T/16 = 5/16
=> T = 5
Therefore the pipe B should be kept close for 5 minutes.
check Approved by eNotes Editorial