Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time will the empty tank be completely filled, if both the pipes are opened together ?

12 hours

Pipe A empties a half-filled tank in $3$ hours

Half tank emptied in $3$ hours

Emptying rate of A

$=\frac{1/2}{3}=\frac{1}{6}$ tank per hour (emptying)

Pipe B fills the tank in $4$ hours

Filling rate of B

$=\frac{1}{4}$ tank per hour

Net rate when both are open

$=\frac{1}{4}-\frac{1}{6}$

$=\frac{3-2}{12}=\frac{1}{12}$ tank per hour

Time required to fill $1$ tank

$=\frac{1}{1/12}=12$ hours

The empty tank will be filled in $12$ hours.