Online Pipes and Cisterns Exercise with Correct Answer Key and Solutions
Useful for all Competitive Exams
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Question 1 of 20
Two taps can fill a tank in 12 and 18 minutes respectively. Both are kept open for 2 minutes and the first is turned off. In how many minutes more will the tank be filled?
Part filled by first tap in 1 min
Part filled by second tap in 1 min
since part of tank is filled by second tap in 1min.
∴ part of tank is filled by second tap in 1 min.
= 13 min.
Question 2 of 20
Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together, but at the end of 3 minutes, ‘B’ is turned off. How much time will the cistern take to fill?
In one min, (A + B) fill the cistern
In 3 min, (A + B) fill the cistern
since part filled by A in one min.
∴ ½nd part filled by A in 10 × ½ = 5 minutes
∴ Total time = 3 + 5 = 8 min.
Question 3 of 20
Two fill pipes A and B can fill a cistern in 12 and 16 minutes respectively. Both fill pipes are opened together, but 4 minutes before the cistern is full, one pipe A is closed. How much time will the cistern take to fill?
Let cistern will be full in x min. Then,
part filled by B in x min + part filled by A in
(x – 4) min = 1
Question 4 of 20
Two fill taps A and B can separately fill a cistern in 45 and 40 minutes respectively. They started to fill a cistern together but tap A is turned off after few minutes and tap B fills the rest part of cistern in 23 minutes. After how many minutes, was tap A turned-off?
Let A was turned off after x min. Then,
cistern filled by A in x min + cistern filled by B in
(x + 23) min = 1
Question 5 of 20
Three fill pipes A, B and C can fill separately a cistern in 3, 4 and 6 minutes respectively. A was opened first. After 1 minute, B was opened and after 2 minutes from the start of A, C was also opened. Find the time when the cistern will be full?
Let cistern will be full in x min. Then,
part filled by A in x min + part filled by B in
(x – 1) min + part filled by c in (x – 2)min = 1
Question 6 of 20
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, then the tank will be full in:
(A + B)’s 1 hour’s work
(A + C)’s 1 hour’s work
Part filled in 2 hrs
Part filled in 6 hrs
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
∴ Total time taken to fill the tank
= (6 + 1) hrs = 7 hrs.
Question 7 of 20
A hot pipe takes 3 minutes longer to fill a tank than the cold pipe. Together they take 6 minutes 40 seconds. Time taken by the cold pipe alone to fill the tank is :
Let cold pipe take X minutes, then hot pipe will take (X + 3) minutes.
40X + 60 = 3X (X + 3)
⇒ 40X + 60 = 3X² + 9X
⇒ 3X² – 31X – 60 = 0
⇒ X = 12 minutes
Question 8 of 20
Two pipes P and Q would filled a cistern in 24 hours and 32 hours respectively . If both pipes are opened together, find when the first pipe must be turned off so that the cistern may be just filled in 16 hours?
If two pipes function simultaneously, the reservoir is filled in 12 hrs. One pipe fills the reservoir 10 hrs faster than the other .How many hours does the faster pipe take to fill the reservoir?
Let the faster pipe fills the tank in x hrs.
Then the slower pipe fills the tank in x + 10 hrs.
When both of then are opened, the reservoir will be filled in
⇒ x² – 14x – 120 = 0
∴ x = 20, – 6
But x can’t be – ve, hence the faster pipe will fill the reservoir in 20 hrs.
Question 10 of 20
A cistern has two taps (which fill it in 12 min and 15 min, respectively) and an exhaust tap. When all three taps are opened together, it takes 20 min to fill the empty cistern. How long will the exhaust tap take to empty it?
Let the exhaust tap empties the tank in x minutes.
⇒ x = 10 min
Question 11 of 20
One tap can fill a cistern in 2 hours and another can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are open?
Work of both tap for 1 hour
Hence, both tap will fill the cistern in 6 hours.
Question 12 of 20
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is :
Work done by the waste pipe in 1 minute
= [–ve sign means emptying]
∴ Volume of ¹⁄₄₀ part
= 3 gallons.
Volume of whole
= (3 × 40) gallons
= 120 gallons.
Question 13 of 20
Tap ‘A’ can fill a water tank in 25 minutes, tap ‘B’ can fill the same tank in 40 minutes and tap ‘C’ can empty that tank in 30 minutes. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied?
Tank filled in 1 minute
∴ tank will be filled complete in minutes
Question 14 of 20
A water tank is ⅖th full. Pipe A can fill the tank in 10 minutes and the pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Since pipe A in 1 minute fills ¹⁄₁₀ part and Pipe B in 1 min. empties ⅙ part
∴ Pipe A + B in 1 min
Since ¹⁄₁₅ part gets emptied in 1 min
∴ ⅖ part is emptied in
15 × ⅖ min = 6 min
Question 15 of 20
A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be?
If both the pumps are opened together, then the tank will be emptied because the working efficiency of pump emptying is more than that of the pump filling it. Thus in 1 min net work done
or the tank will be emptied in 16 min
⇒ ½ tank will be emptied in 8 min.
Question 16 of 20
A pipe can fill a tank in 15 minutes and another one in 10 minutes. A third pipe can empty the tank in 5 minutes. The first two pipes are kept open for 4 minutes in the beginning and then the third pipe is also opened. In what time will the tank be emptied?
Proportion of the volume of the tank filled by both the pipes in 4 min
= ⅔rd of the tank.
Volume of the tank filled by all the pipes working together
i.e. 1/30 tank is emptied in 1 min.
Question 17 of 20
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Net part filled in 1 hour
∴ The tank will be full in
Question 18 of 20
A, B, C are pipes attached to a cistern. A and B can fill it in 20 and 30 minutes, respectively, while C can empty it in 15 minutes, If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?
1 minute’s work of each of the three pipes
i.e., work of 3 pipes for 3 minutes
∴ Work of 3 pipes for 55 minutes each
∴ Remaining part to be filled
Now, pipe A will fill 1/20 of the cistern in next 1 minute.
∴ Remaining portion to be filled by pipe B
∴ Time taken by pipe B to fill 1/30 of the cistern = 1/30 × 30 = 1min
Hence, total time
= (55 × 3) + 1 + 1
= 167 min.
Question 19 of 20
Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes, Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. The number of inlet pipes is
Total number of pipes = 6 (given)
Let number of inlet pipes = x
∴ number of outlet pipes = 6 –x
Now, Inlet pipe fill the tank in 9 hours and outlet pipe empty it in 6 hours.
∴ Total part filled in 1 hour
When all the pipes are opened.
But given total part filled in 9 hr
⇒ 15x = 60 ⇒ x = 4
Hence, number of inlet pipes = 4.
Question 20 of 20
Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. In how much time, will the tank be full?