Pipe A can completely fill an empty tank in 11 hours. Pipe B can empty the same completely filled tank in 15 hours. If they are opened together, in how much time the empty tank will get filled?

Let's assume the capacity of the tank is 165 units.

Pipe A can completely fill an empty tank in 11 hours.

The efficiency of pipe A = $$\frac{165}{11}$$ = 15 units/hour

Pipe B can empty the same completely filled tank in 15 hours.

The efficiency of pipe B = $$\frac{165}{15}$$ = -11 units/hour [Here negative sign represents that pipe is emptying the tank.]

Time taken by both the pipes together to fill the tank = $$\frac{165}{15-11}$$ = $$\frac{165}{4}$$

= $$41\frac{1}{4}$$

= 41 hours 15 minutes       [Here one fourth means that $$\frac{1}{4}$$ of 1 hour which will be 15 minutes.]