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
Pipe P can fill $\frac{2}{3}$ part of a tank in 16 hours, and pipe Q can fill $\frac{5}{6}$ part of the same tank in 20 hours. Both P and Q were kept open for 2 hours, then both were closed. Pipe R alone was then opened and it emptied the water in the tank in 8 hours. Pipes P, Q and R together can fill the empty tank in:
- Pipe A can fill a tank in 18 hours, pipe B can fill the same tank in 30 hours and pipe C can fill the same tank in 18 hours. The time taken by them to fill the same tank if they operate together is::
Pipe P can fill $\frac{2}{3}$ part of a tank in 24 hours, and pipe Q can fill $\frac{2}{3}$ part of the same tank in 16 hours. Both P and Q were kept open for 4 hours, then both were closed. Pipe R alone was then opened and it emptied the water in the tank in 5 hours. Pipes P, Q and R together can fill the empty tank in:
- Pipe P can fill $\frac{5}{7}$ part of a tank in 30 hours, and pipe Q can fill $\frac{2}{5}$ part of the same tank in 28 hours. Both P and Q were kept open for 7 hours, then both were closed. Pipe R alone was then opened and it emptied the water in the tank in 8 hours. Pipes P, Q and R together can fill the empty tank in:
Pipe P can fill $\frac{3}{8}$ part of a tank in 21 hours and pipe Q can fill $\frac{2}{7}$ part of the same tank in 16 hours. Both P and Q were kept open for 2 hours, then both were closed. Pipe R alone was then opened and it emptied the water in the tank in 3 hours. Pipes P, Q and R together can fill the empty tank in:
