Two pipes A and B can fill a tank in 15 minutes and 20 minutes, respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
14 min 40 sec
To determine the total time required to fill the tank, consider the following steps:
Step 1: Calculate the rates of pipes A and B.
- Pipe A can fill the tank in 15 minutes, so the rate of Pipe A = 1/15 of a tank per minute.
- Pipe B can fill the tank in 20 minutes, so the rate of Pipe B = 1/20 of a tank per minute.
Step 2: Determine the amount of tank filled in the first 4 minutes with both pipes open.
- Combined rate of pipes A and B = (1/15 + 1/20) of a tank per minute.
- To find a common denominator: LCM of 15 and 20 is 60.
- Pipe A rate = 4/60, Pipe B rate = 3/60.
- Combined rate = (4/60 + 3/60) = 7/60 of a tank per minute.
- In 4 minutes, the part of the tank filled = 4 * (7/60) = 28/60 = 7/15 of the tank.
Step 3: Determine the remaining part of the tank to be filled by Pipe B alone.
- The remaining part = 1 - 7/15 = 8/15 of the tank.
Step 4: Calculate the time taken by Pipe B to fill the remaining part of the tank.
- Pipe B fills 1/20 of the tank per minute.
- Time required = (8/15) / (1/20) = (8/15) * 20 = 32/3 minutes = 10 minutes and 40 seconds.
Step 5: Calculate the total time.
- Total time = 4 minutes + 10 minutes 40 seconds = 14 minutes and 40 seconds.
Therefore, the total time required to fill the tank is 14 minutes and 40 seconds.
Important Questions from Pipe and Cistern
Pipes A, B and C can fill a tank in 20, 30 and 60 hours, respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 9 a.m., respectively, on the same day. When will the tank be full?
There are two water taps in a tank which can fill the empty tank in 12 hours and 18 hours respectively. It is seen that there is a leakage point at the bottom of the tank which can empty the completely filled tank in 36 hours. If both the water taps are opened at the same time to fill the empty tank and leakage point was repaired after 1 hour, then in how much time the empty tank will be completely filled?
Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All the three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours. All three pipes are opened together, but after 4 hours pipe B is closed. In how many hours, the empty tank will be completely filled?
Pipes A and B can fill a tank in 43.2 minutes and 108 minutes, respectively. Pipe C can empty it at 3 litres/minute. When all the three pipes are opened together, they fill the tank in 54 minutes. The capacity (in litres) of the tank is:
