A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time the cistern will get filled?

Question: A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time the cistern will get filled?

Solution:
The cistern fill in 1 hour = ( 1/6 ) - ( 1/9 ) part = 1/18 part
The cistern fill 1/18 part = 1 hour
The cistern fill full = ( 1 × 18 ) /1 hour = 18 hours