Pipes A and B can fill a tank in 20 hours and 30 hours respectively and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, how much time will he needed to make the tank full ?

$17\frac{1}{7} hours $

The correct answer is Option (3) → $17\frac{1}{7}$ hours

Filling Rate of A = $\frac{1}{20}$ tank per hour.

Filling Rate of B = $\frac{1}{30}$ tank per hour.

Filling Rate of C = $\frac{1}{40}$ tank per hour.

Net Rate = Rate of A + Rate of B - Rate of C

$=\frac{1}{20}+\frac{1}{30}-\frac{1}{40}$

$=\frac{7}{20}$

$\text{Time} = \frac{1}{\text{Net Rate}}=\frac{7}{20}=17\frac{1}{7}$ hours