A cistern can be filled by an inlet pipe in 20 hours and can be emptied by an outlet pipe on 25 hours. Both the pipes are opened. After 10 hours, the outlet pipe is closed, the total time to fill the tank is :

28 hours

The correct answer is Option (4) → 28 hours

Inlet pipe rate = $\frac{1}{20}$ per hour

Outlet pipe rate = $\frac{1}{25}$ per hour

After 10 hours

$=10\left(\frac{1}{20}-\frac{1}{25}\right)=\frac{1}{10}$ of cistern

Remaining part to be filled = $1-\frac{1}{10}=\frac{9}{10}$

Time taken now when only inlet pipe is open:

Time = $\frac{0.9}{\frac{1}{20}}=\frac{9}{10}×20=18$ hours

Therefore, total time = $18+10=28$ hours