Pipes and Cistern problems
- 1. A tap can fill a cistern in 8 hours and another can empty it in 16 hours. If both the taps are opened simultaneously, the time (in hours) to fill the tank is?
Options- A. 8
- B. 10
- C. 16
- D. 24 Discuss
Correct Answer: 16
Explanation:
Part filled by intel in 1 hour = 1/8
Part emptied by outlet in 1 hour = 1/16
Net filling in 1 hour = (1/8 - 1/16) = 1/16
? Time taken to fill the tank = 16 hours
- 2. Pipes A and B can fill a tank in 10 hours and 15 hours respectively. Both together can fill it in?
Options- A. 121/2 hours
- B. 6 hours
- C. 5 hours
- D. None of these Discuss
Correct Answer: 6 hours
Explanation:
Part filled by A in 1 hour = 1/10
Part filled by B in 1 hours = 1/15
Part filled by (A + B) in 1 hour = (1/10 + 1/15) = 5/30 = 1/6
? Both pipes together can fill the tank in 6 hours.
- 3. Three are two taps to fill a tank while a third to empty it. When the third tap is closed, they can fill the tank in 10 minutes and 12 minutes respectively. If all the three taps be opened, the tank is filled in 15 minutes. If the first two taps are closed, in what time can the third tap empty the tank when it is full?
Options- A. 7 min.
- B. 9 min. and 32 sec.
- C. 8 min. and 34 sec.
- D. 6 min. Discuss
Correct Answer: 8 min. and 34 sec.
Explanation:
Part emptied by the third pipe in 1 min (1/10 + 1/12) - 1/25 = 7/60
So, the full tank will be emptied by third pipe in = (60/7) min. = 8 min. 34 ec.
- 4. A tap can fill a tank in 25 minutes and another can empty it in 50 minutes. Find whether the tank will be filled up or emptied and in how many minutes?
Options- A. Tank is emptied in 20 minutes
- B. Tank is filled up in 50 minutes
- C. Tank is filled up in 20 minutes
- D. Tank is emptied in 25 minutes Discuss
Correct Answer: Tank is filled up in 50 minutes
Explanation:
T = (25 x 50) / (50 - 25) = + 50 minutes
+ ve sign shows that tank is filled up in 50 minutes.
- 5. Two pipes A and B can fill a tank in 18 and 6 h, respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Options- A. 41/2h
- B. 7 h
- C. 6 h
- D. 10 h Discuss
Correct Answer: 41/2h
Explanation:
Part filled by A in 1 h = 1/18
Part filled by B in by 1 h = 1/6
Part filled (A + B) in 1 h =1/18 + 1/6 = (1 + 3)/18 = 4/18 = 2/9
Hence, both the pipes together will fill the tank in 9/2 h or 41/2 h
- 6. A cistern can be filled up in 4 h by an inlet A. An outlet B can empty the cistern in 8 h. If both A and B are opened simultaneously, then after how much time will the cistern get filled?
Options- A. 5 h
- B. 7 h
- C. 8 h
- D. 6 h Discuss
Correct Answer: 8 h
Explanation:
Part filled by A in 1 h = 1/4
Part emptied by B in 1 h = 1/8
Part filled by (A + B) In 1 h = 1/4+ ( -1/8 ) = 1/4 - 1/8 = (2 - 1)/8 = 1/8
? Required time to fill the cistern = 8
- 7. Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?
Options- A. 33/14 h
- B. 21/2 h
- C. 39/14 h
- D. 21/14 h Discuss
Correct Answer: 21/2 h
Explanation:
Part filled by A in 1 h = 1/5
Part filled by B in 1 h = 1/6
Part filled by C in 1 h = 1/30
Net part filled by ( A + B + C ) in h 1 = ( 1/5 + 1/6 + 1/30 )
= (6 + 5 + 1)/30 = 12/30 = 2/5
? Required time to fill the tank = 5/2 = 21/2 h
- 8. A tap can fill an empty tank in 12 h and a leakage can empty the tank in 20 h. If tap and leakage both work together, then how long will it take to fill the tank?
Options- A. 25 h
- B. 40 h
- C. 30 h
- D. 35 h Discuss
Correct Answer: 30 h
Explanation:
Part filled by tap in 1 h = 1/12
Part emptied by leak in 1 h = 1/20
Net part filled in 1 h when both (tap and leakage) work = 1/12 - 1/20
= (5 - 3)/60 = 2/60 = 1/30
? Required time to fill the tank = 30 h
- 9. Three taps A, B and C together can fill an empty cistern in 10 min . The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?
Options- A. 16 min
- B. 24 min
- C. 32 min
- D. 40 min Discuss
Correct Answer: 24 min
Explanation:
Part filled by (A + B + C ) in 1 min = 1/10
Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/40
Part filled by (A+B) in 1 min = 1/30 + 1/40 = (4 + 3)/120 = 7/120
? Part filled by C in 1 min = 1/10 - 7/120 = (12 - 7)/120 = 5/120 = 1/24
? Tap C will fill the cistern in 24 min.
- 10. Two pipes A and B can fill a cistern in 15 and 20, respectively. Both the pipes are opened together, but after 2 min, pipe A is turned off. What is the total time required to fill the tank?
Options- A. 46/3 min
- B. 52/3 min
- C. 43/3 min
- D. 41/3 Discuss
Correct Answer: 52/3 min
Explanation:
Part filled by both in 2 min = 2 x ( 1/15 + 1/20 ) = 2 x ( 4 + 3)/60 = 7/30
Part unfilled = 1 - 7/30 = (30 - 7)/30 = 23/30
Now, B fills 1/20 part in 1 min.
? 23/30 part will be filled by B in (20 x 23)/30 min or in 46/3 min.
? Required time taken to fill the tank = 2 + 46/3 = 52/3 min.
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