A tank can be filled by pipe A in 30 minutes and by pipe B in 24 minutes. Outlet pipe C can empty the full tank in X minutes.
If the tank is empty initially and if all the three pipes A, B and C are opened simultaneously, the tank will NEVER be full. Give the maximal possible value of X.
The maximum possible value of X is 13 minutes 20 seconds.
In one minute,
pipe A can fill 1/30 part of the tank.
pipe B can fill 1/24 part of the tank.
Thus, the net water level increase in one minute is
= 1/30 + 1/24
= 3/40 part of the tank
In order to keep the tank always empty, outlet pipe C should empty at least 3/40 part of the tank in one minute. Thus, pipe C can empty the full tank in 40/3 i.e. 13 minutes 20 seconds.
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