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- Question
- A pipe can fill a cistern in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then third pipe is also opened. In what time is the cistern emptied?
Options- A. 30 min.
- B. 33 min.
- C. 371 / 2 min.
- D. 45 min.
- Correct Answer
- 45 min.
ExplanationPart filled in 5 min. = 5 x (1/12 + 1/15) = 5 x 9/60 = 3/4
Part emptied in 1 min. (when all the pipes are opened) = 1/6 - (1/12 + 1/15) = (1/6 - 3/20) = 1/60
Now, 1/60 part is emptied in 1 min. 3/4 part will be emptied in (60 x 3/4) = 45 min. - 1. Three pipes A, B and C can fill a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 1 hour, B was opened and after 2 hours from the start of A, C also opened . Find the time in which the cistern is just full?
Options- A. 2 hrs.
- B. 4 hrs.
- C. 2 hrs. 52 min.
- D. 4 hrs. 52 min. Discuss
- 2. Two pipes, P ans Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options- A. 81/4 minutes
- B. 11 1/4 minutes
- C. 73/4 minutes
- D. 83/4 minutes Discuss
- 3. A cistern has 3 pipes A, B and C, A and B can fill it in 2 and 3 hours respectively. C is a waste pipe. If all the 3 pipes be opened at once, 7/24 of the cistern will be filled up in 30 minutes. In what time can C empty the full cistern?
Options- A. 3 hours
- B. 4 hours
- C. 5 hours
- D. 6 hours Discuss
- 4. A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full, in what time will the leak empty it?
Options- A. 80 hours
- B. 85 hours
- C. 90 hours
- D. 95 hours Discuss
- 5. 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. The time taken to fill the tank is?
Options- A. 12 hours
- B. 131/2
- C. 16 hours
- D. 18 hours Discuss
- 6. A leak in the bottom of a tank can empty the full tank in 6 hours. An Inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the Inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank is?
Options- A. 5260 litres
- B. 5760 litres
- C. 5846 litres
- D. 6970 litres Discuss
- 7. Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes?
Options- A. 6 min.
- B. 8 min.
- C. 10 min.
- D. 12 min. Discuss
- 8. A water tank is 2/5th 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?
Options- A. 6 minutes to empty
- B. 6 minutes to fill
- C. 9 minutes to empty
- D. 9 minutes to fill Discuss
- 9. Top A can fill a water tank in 25 minutes, tap B can fill the same tank in 40 minutes and tap C can empty the 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?
Options- A. 32/13
- B. 155/13
- C. 82/13
- D. 3111/19 Discuss
- 10. A cistern can be filled by two pipes. A and B in 12 minutes and 14 minutes respectively and can be emptied by a third pipe C in 8 minutes. If all the taps be turned on at the same moment, what part of cistern will remain unfilled at the end of 7 minutes?
Options- A. 5/24
- B. 19/24
- C. 7/24
- D. 17/24 Discuss
Pipes and Cistern problems
Search Results
Correct Answer: 4 hrs. 52 min.
Explanation:
[(A's 1 hour work) + (A + B)'s 1 hour work]
= (1/10) + [(1/10) + (1/12)] = 17/60
Remaining part = 1 - (17/60) = 43/60
Now, (A + B + C)'s 1 hour work = (1/10) + (1/12) + (1/15) = 1/4
1/4 part is filled by 3 pipes in 1 hour.
43/60 part will be filled by them in 4 x (43/60) hrs. = 2 hours 52 min.
? Total time taken to fill the cistern = 4 hours 52 min.
Correct Answer: 81/4 minutes
Explanation:
12(1 - t/25) = 3
? t = 45/4 = 111/4 minutes
? Required answer = 111/4 - 3
= 81/4 minutes
Correct Answer: 4 hours
Explanation:
? 7/24 of the cistern will be filled up in 1/2 hr.
? The whole of the cistern will be filled up in (1/2) x (24/7) = 12/7 hrs.
Let the pipe C be empty the whole cistern in h hours
Now, applying the given rule we have,
(2 x 3 x h) / (3 x h + 2 x h - 2 x 3) = 12/7
or 42h = 60h - 72
? h = 4 hours.
Correct Answer: 90 hours
Explanation:
Let the leak empty the full cistern in N hours
Now, applying the given rule (9 x N) / (N - 9) = 9 + 1
or N = 90 hours.
Correct Answer: 12 hours
Explanation:
Part filled in 10 hours = 10 x (1/15 + 1/20 - 1/25) = 23/30
Remaining part = (1 - 23/30) = 7/30
Now, (1/15 + 1/20) part is filled by A and B in 1 hr.
7/30 part be filled them in (60/7) x (7/30) = 2 hrs.
? Total time taken to fill the tank = (10 + 2) hrs. = 12 hrs.
Correct Answer: 5760 litres
Explanation:
Part filled by inlet in 1 hour = (1/6 - 1/8) = 1/24
So, the inlet can fill the tank in 24 hours
? Capacity of the tank = Water that flows in 24 hours = (4 x 24 x 60) liters = 5760 liters
Correct Answer: 8 min.
Explanation:
Let Y be closed after T min
Then, T x (1/ 24 + 1/32) + (18 - T) x 1/24 = 1
? (7 x T)/96 + (18 - T)/24 = 1
or 7T + 72 - 4T = 96.
? 3T = 24
or T = 8 min.
Correct Answer: 6 minutes to empty
Explanation:
Time taken to fill or empty the whole tank = (6 x 10) /(6 - 10) = - 15 minutes
- ve sign shows that the tank will be emptied.
? 2/5th full of the tank will be emptied in 15 x 2/5 = 6 minutes
Correct Answer: 3111/19
Explanation:
Required answer = (25 x 40 x 30) / (40 x 30 + 25 x 30 - 25 x 40)
= 600 / 19 = 3111/19 minutes
Correct Answer: 19/24
Explanation:
Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes
? In 7 minutes 5/168 x 7 = 5/24 part of the tank will be filled
? Requied answer = 1 - 5/24 = 19/24 part
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