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
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?
