Two pipes A and B can fill a cistern in 15 hours and 25 hours respectively. Another pipe C can empty the full tank in 30 hours. If all the pipes are opened together, then the time needed to fill the cistern fully is :

$13\frac{7}{11}$ hours

The correct answer is Option (2) → $13\frac{7}{11}$ hours

Rate of Pipe A = $\frac{1}{15}$ cistern per hour

Rate of Pipe B = $\frac{1}{25}$ cistern per hour

Rate of Pipe C = $\frac{-1}{30}$ cistern per hour

Combine rate = $\frac{1}{15}+\frac{1}{25}-\frac{1}{30}=\frac{11}{150}$

Time = $\frac{150}{11}=13\frac{7}{11}$ hours