Pipe A can fill a tank in 10 hours. Pipe B can fill the same tank in 12 hours. Pipe C can empty the full tank in 16 hours. All the pipes are opened at 8 : 00 A.M.and Pipe A and B are closed at 10 : 00 A.M. After how much time from starting will the tank be empty?

Let's assume the total capacity of the tank is 240 units.

Pipe A can fill a tank in 10 hours.

Efficiency of Pipe A = $$\frac{240}{10}$$ = 24 units/hour

Pipe B can fill the same tank in 12 hours.

Efficiency of Pipe B = $$\frac{240}{12}$$ = 20 units/hour

Pipe C can empty the full tank in 16 hours.

Efficiency of Pipe C = $$\frac{240}{16}$$ = -15 units/hour (Here negative sign represents that this pipe is used to empty the tank.)

All the pipes are opened at 8 : 00 A.M.and Pipe A and B are closed at 10 : 00 A.M.

Tank filled by all the pipes in 2 hours = $$2\times(24+20-15)$$

= $$2\times29$$

= 58 units

Now only pipe C is working. So the time taken by pipe C to empty the tank which is 58 units filled = $$\frac{58}{15}$$

= $$3\frac{13}{15}$$ hours

Time from starting, the tank will be emptied = $$2+3\frac{13}{15}$$ hours

= $$5\frac{13}{15}$$ hours

= 5 hours $$\frac{13}{15}\times60$$ minutes

= 5 hours 52 minutes