A cistern can be filled by a tap in 6 hours and emptied by an outlet pipe in 7.5 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?
30 hours
To solve this problem, we need to determine the time it takes to fill the cistern when both the tap and the outlet pipe are open simultaneously. First, we calculate the rate at which each operates:
- The tap can fill the cistern in 6 hours, thus it fills of the cistern per hour.
- The outlet pipe empties the cistern in 7.5 hours, meaning it empties per hour.
To find their combined rate, subtract the outlet pipe's rate from the tap's rate:
This combined rate means the cistern is filled at a rate of per hour when both are open. Therefore, the cistern will be completely filled in:
30 hours
Important Questions from Pipe and Cistern
A pipe can fill a cistern in 20 minutes where as the cistern when full can be emptied by a leak in 28 minutes. When both are opened, The time taken to fill the cistern is:
‘A’ pipe can empty a tank in 20 minutes. The second pipe ‘B’ has a diameter twice as that of ‘A’. If both A & B pipe are attached to the tank how much time will be required to empty the tank?
Pipes A and B can empty a full tank in 16 hours and 24 hours, respectively. Pipe C alone can fill the empty tank in 4 hours. If A, B and C are opened together, the tank will be 35% full after :
Pipes A and B can fill a tank in 36 minutes and 45 minutes, respectively. Both these pipes were opened simultaneously. After 20 minutes, a leak at the bottom of the tank was spotted which was immediately sealed. The tank was full in another 15 minutes. The leak alone can empty the full tank in:
A cistern has a leak which would empty it in 6 hours. A tap is turned on which admits 10 litres of water per minute into the cistern. When it is full it is now emptied in 10 hours. What is the capacity (in litres) of the cistern?
