Pipes and Cistern problems
- 1. Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill it in 7 hours. The time taken by C alone to fill the cistern is?
Options- A. 10 hours
- B. 12 hours
- C. 14 hours
- D. 16 hours Discuss
Correct Answer: 14 hours
Explanation:
Part filled in 2 hours = 2 x 1/6 = 1/3
Remaining part = (1 - 1/3) = 2/3
(A + B)'s 7 hour's work = 2/3
? (A + B)'s 1 hour's work = (2/3 x 1/7) = 2/21
(A + B + C)'s 1 hour's work = 1/6
C's 1 hours work = (1/6 - 2/21) = 1/14
Hence, C alone can fill the cistern in 14 hours.
- 2. If two function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Options- A. 25 hours
- B. 28 hours
- C. 30 hours
- D. 35 hours Discuss
Correct Answer: 30 hours
Explanation:
Suppose that one pipe takes N hours to fill the reservoir. Then another pipe takes (N - 10) hours.
? 1/N + 1/(N - 10) = 1/12
? 12(N - 10 + N) = N(N - 10)
or N2 - 34N + 120 = 0
or (N - 30)(N - 4) = 0
? N = 30 or N = 4
So, the faster pipe takes 30 hours to fill the reservoir.
- 3. 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
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.
- 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
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.
- 5. 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
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.
- 6. 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
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
- 7. 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
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.
- 8. 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. Discuss
Correct Answer: 45 min.
Explanation:
Part 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.
- 9. 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
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
- 10. 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
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.
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