The inlet pipe is designed to fill the cistern, whereas the outlet pipe is intended for emptying it. If a pipe can fill a tank in x hours, then the rate at which the pipe can fill the same tank in 1 hour is equal to 1/x.
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Example 1: Two pipes A and B are connected to a container. Pipe A can empty the container in 20 minutes and pipe B can empty the container in 30 minutes. Both A and B are opened together. Find out the time to empty the container completely?
(a) 12 mins
(b) 14 mins
(c) 10 mins
(d) 7 mins
Ans: (a)
Let the size of the container be = 60 units [LCM (20, 30)]
Efficiency of pipe A = 60/20 = 3 units
Efficiency of pipe B =60/30 = 2 units
Combined efficiency of pipe A and pipe B = 5 units/min
So, time required to empty the container with both pipes = 60/5 = 12 mins
Example 2: A pipe takes 5 hours to fill a water tank but because of leakage, it takes 3 hours more. Find out the number of hours taken by leakage pipe to empty the full water tank?
(a) 40/3 hrs
(b) 3/40 hrs
(c) 3/47 hrs
(d) 2/51 hrs
Ans: (a)
Water tank filled in 5 hours = 1/5
Now, due to outlet pipe, 1 hour part filled = 1/8
Part of the water tank emptied in 1 hour
So, the leak will empty the full water tank in 40/3 hrs
Example 3: There are three pipes A, B and C, which can fill the tank in 10 hours. All the three pipes were opened for together for 5 hours, C is closed and inlets A and B fill the remaining part in 12 hours. Find the time taken by C alone to fill the tank.
(a) 18 hrs 7 mins
(b) 17 hrs 8 mins
(c) 18 hrs
(d) 17 hrs
Ans: (b)
Part of the tank filled by the pipes A, B and C in 1 hour = 1/10
Part of the tank filled by the pipes A, B and C in 5 hours
Remaining portion of tank to be filled =
Now, when A and B are open
Part of the tank filled by A and B in 1 hour
Therefore, part of the tank filled by C in 1 hour
Time taken by C alone hours which can be written as 17 hrs 8 mins
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1. What is the concept of inlet and outlet pipes in pipes and cisterns? |
2. How do you calculate the time taken to fill a cistern when both the inlet and outlet pipes are open? |
3. Can the rate of filling and emptying of a cistern be given in terms of the capacity of the cistern? |
4. How do you calculate the time taken to fill a cistern when the inlet and outlet pipes are connected in series? |
5. Can the rates of filling and emptying be given in terms of fractions? |
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