Two pipe A and B can fill a tank in 1/2 hour and 1 hour respectively. A pipe C can empty the tank in 2 hours. IF all three pipe are opened simultaneously, how long does it take to fill the empty tank ?

24 min

The correct answer is option (1) : 24 min

Pipe A can fill the tank in $\frac{1}{2}$ hr in 30 min

Pipe B can fill the tank in 1 hr i.e 60 min.

Pipe C can empty the tank in 2 hrs i.e 120 min.

When all the 3 pipes are opened simultaneously, then part of tank filled in 1 min

$=\frac{1}{30}+\frac{1}{60}-\frac{1}{120}=\frac{4+2-1}{120}=\frac{5}{120}=\frac{1}{24}$

∴ The time required to fill the empty tank = 24 min