A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the ...
Inlet pipe Efficiency = 100/(8/6) = 75%
Outlet pipe Efficiency = 100/(4) = 25%
Net Efficiency = 75 – 25 = 50%(1/3)filled
2/3 filled = 100%
Required time = 100/50 = 2 hours
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A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the ...
A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the ...
Problem Solving Strategy:
- Determine the filling rate of the inlet pipe
- Determine the draining rate of the outlet pipe
- Determine the net filling rate when both pipes are opened
- Use the net filling rate to determine the time to fill the tank
Solution:
Let the total capacity of the cistern be C.
When the inlet pipe is plugged, the outlet pipe can empty the cistern in 4 hours. Therefore, the draining rate of the outlet pipe is:
outlet pipe draining rate = C/4
When the outlet pipe is plugged, the inlet pipe can fill the cistern in 1 hour 20 minutes, which is equivalent to 4/3 hours. Therefore, the filling rate of the inlet pipe is:
inlet pipe filling rate = C/(4/3) = 3C/4
When both pipes are opened simultaneously, the net filling rate is:
net filling rate = inlet pipe filling rate - outlet pipe draining rate
= 3C/4 - C/4
= C/2
This means that the cistern will fill at a rate of C/2 per hour.
At the start, the cistern is one-third filled, which is equivalent to C/3. Therefore, the remaining capacity to be filled is:
remaining capacity = C - C/3 = 2C/3
Using the net filling rate, the time to fill the remaining capacity is:
time to fill = remaining capacity / net filling rate
= (2C/3) / (C/2)
= 4/3 hours
= 1 hour 20 minutes
Therefore, the cistern will fill completely in 1 hour 20 minutes after both pipes are opened simultaneously.
The correct answer is option 'B', which is 2 hours.