Pipes X,Y and Z are fitted to a pank. X and Y can fill a tank in 18 hours and 24 hours respectively. Z is an emptying pipe which can empty the tank in 9 hours. All the pipes are opened simultaneously when the tank is half full. The tank would be

Options

A. filled in 72 hours
B. empitied in 72 hours
C. filled in 36 hours.
D. emptied in 36 hours

Answer

D

Explanation

Part of the tank which X and Y can fill in one hour =`(1)/(18)+(1)/(24)=(7)/(72)`
Part of the tank that Z can empty in one hour `=(1)/(9)=(8)/(72)`
Emptying rate of `Zgt` filling rate of X and Y.
`:.` The tank will be emptied
Part of it emptied eac hour `=(8)/(72)-(7)/(72)=(1)/(72)`
Time taken to empty `(1)/(2)` of the tank
`=((1)/(2))/((1)/(72))` hours
`=36` hours