An inlet pipe and an outlet pipe are taking to fill and drain a cistern, respectively, for an hour each at a time, starting with the inlet pipe when the cistern is empty. It takes the inlet pipe 15 hours to fully fill the empty cistern, whereas the outlet pipe can drain the filled cistern completely in 21 hours. How many hours will it take for the cistern to be full?

Option 4 : 99

Calculation:

Inlet pipe can fill a cistern in = 15 hours

∴ In 1 hour the inlet pipe can fill = 1/15

Outlet pipe can empty a cistern in = 21 hours

∴ In 1 hour the outlet pipe can empty = 1/21

In 1^st our cistern is filled = 1/159

In the next every 2 hours cistern is filled = (1/15 - 1/21) = 2/105

Let, the cistern will be filled in next 2x hours

According to the question,

⇒ 1/15 + 2x/105 = 1

⇒ 2x/105 = 1 - 1/15

⇒ 2x = 14/15 × 105

⇒ 2x = 98

∴ It will take (1 + 98) = 99 hours to fill the cistern

⇒ 98 hours

Total required time = (98 + 1) = 99 hours

∴ It will take 99 hours to make the cistern full.