Answer / guest

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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