In the previous article we learned about Time and Work. The question arises here that are “Pipes and cisterns” related to Time and Work? The answer is – Yes. Pipes and Work are an extended version of Time and Work. The only difference here is that instead of men the work is done by the pipes.
Let us understand this with the help of an example.
Example: If a pipe A can fill a tank in 10 minutes, then in 1 minute, it will fill 1/10th part.Similarly, if a pipe B can fill the same tank in 15 minutes, then in 1 minute, it will fill 1/15th part. Now if we open both the pipes together, then the part of the tank filled in one minute will be
Hence, if both the pipes are opened together, then the tank will be filled in 6 minutes.This is the same logic that we have discussed in Time and Work.
Note (Alternative approach): We can also solve this question by taking the capacity of the tank as some units(usually the LCM of time taken by the pipes).
In the above example, pipe A can fill the tank in 10 minutes and pipe B can fill it in 15 minutes.
Let us take the capacity of the tank as the LCM (10, 15) = 30 litres.
So, the pipe A can fill at 3 litre/min and pipe B can fill at 2 litre/min. Together these two pipes can fill 5 litre in one minute.
So, the time taken to fill the tank is 30/5 = 6 litre.
Example: Now let us say that there is another pipe C in addition to the pipes A and B mentioned above and this pipe C can empty the full tank in 30 minutes. If all the three pipes A, B and C are opened together, then in what time the tank will be filled?
Let us see what happens in this case. Here pipe A can fill the tank in 10 minutes, pipe B can fill it in 15 minutes and pipe C can empty it in 30 minutes.
So, pipe A will fill 1/10th part in 1 minute, pipe B will fill 1/15the part in one minute whereas pipe C will empty 1/30th part in one minute.
Now if all the pipes are opened together, then the part filled in one minute =
Hence, time taken to fill the tank = 15/2 = 7.5 hours.
Note that the value of C is taken negative here. The reason is that pipe C is emptying the tank. So when a pipe fills the tank, the take the work as positive and when it empties a tank then take its wok a negative.
To get a firm hold on the above concepts, solve the exercise given below:
Example 1: A pipe can fill a cistern in 20 hours. Find the part of tank filled in 5 hours.
Solution: If a pipe can fill a complete tank in m hours, then in one hour (1/m)thpart will be filled
And in t time (1/m)×t part will be filled
Here m = 20 and t=5
So, in 5 hours, (1/20)× 5=1/4th part will be filled.
Example 2: A pipe can fill a cistern in 30 minutes. Find the time in which 1/3rd part of cistern will be filled.
Solution: If a pipe can fill a complete tank in 30 minutes then (1/3)rd part of work will be filled in
Example 3: A pipe can empty a cistern in 20 hours. Find the time in which 4/5th part will be emptied.
Solution: If a pipe can empty a complete tank in 20 hours
4/5th part of tank will be emptied in
Example 4: A pipe can fill a tank in 4 hours and another pipe can empty it in 5 hours. If both the pipes are opened,find the time in which tank is filled?
Solution: The tank filled by the first pipe in one hour = 1/4 and the tank emptied by the second pipe in one hour = 1/5. When both the pipes are opened then the part of the tank filled in one hour
Hence it will take 20 hours to fill the tank.
Example 5: A water tank is full.Pipe A can fill the tank in 12 minutes and pipe B can empty it in 4 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?
Solution: Tank filled by pipe A in one minute = 1/12th part and the part emptied by the pipe B in one minute = 1/4th part. Now if both pipes are opened together, then the part filled in 1 minute = Here negative sign shows that the tank will be emptied and not filled if both the pipes are opened. So, the whole tank if it is full can be emptied in 6 minutes. So, to empty 3/5th part, the time required =
Example 6: Two pipes A and B can fill a tank in 16 minutes and 12 minutes, respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes.
Solution: Let the capacity of the tank = LCM (12, 16) = 48 litres.
So, pipe A can fill 3 litre in one minute whereas pipe B can fill 4 litre in one minute. It is required that the tank should be filled in 8 minutes. As pipe B is closed, so pipe A will work for full 8 minutes. In 8 minutes, pipe A will fill 8 × 3 = 24 litre. So, the remaining 48 – 24 = 24 litre will be filled by pipe B and it will take 24/4 = 6 minutes. So, pipe B should be closed after 6 minutes.
Example 7: Two pipes A and B can fill a cistern in 20 minutes and 25 minutes, respectively. Both are opened together but at the end of 5 minutes, B is turned off. How much longer will the cistern take to fill?
Solution: Let the capacity of the tank = LCM (20, 25) = 100 litres. So, pipe A will fill 5 litre in 1 minute and pipe B will fill 4 litre in 1 minute. Now pipe B is closed after 5 minutes.
In 5 minutes, the water filled = 5 × (5+ 4) = 45 litres.
The remaining water 100 – 45 = 55 litre will be filled by pipe A and it will take 55/5 = 11 minutes to fill it. Hence the total time = 11 + 5 = 16 minutes.
Time and Work Questions: Problems on Time and Work you should solve for competitive examination preparation
Welcome to this exercise on Time and Work problems. In this exercise, we build on the basic concepts for Time and Work and explore pipes and cisterns problems. As you prepare for your competitive examinations, you will come across questions on pipes and cisterns. Such questions need optimized tackling and can be solved with ease by using simple tricks and understanding the relationships highlighted in this Time and Work Questions article. The Time and Work Questions and the pipes and cisternproblems exercise comes into the picture where it gives you a chance to practice the highlighted and important concepts related to this Time and Work question type.