Tap A can fill an empty tank in 8 hours if no other tap is open, and tap B can empty the same tank, when filled, in 12 hours, when no other tap is open. Find the time taken to fill the same tank, when empty, if both the taps are opened together.

Total capacity of the tank is 24 units.

Tap A can fill an empty tank in 8 hours if no other tap is open.

Efficiency of Tap A = $$\frac{24}{8}$$ = 3 units/hour

tap B can empty the same tank, when filled, in 12 hours, when no other tap is open.

Efficiency of Tap B = -$$\frac{24}{12}$$ = -2 units/hour [Here negative sign represents that the tap is used for emptying the tank.]

Time taken to fill the same tank, when empty, if both the taps are opened together = $$\frac{24}{3-2}$$

= $$\frac{24}{1}$$

= 24 hours