Pipes and Cistern problems
- 1. 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
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
- 2. 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
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
- 3. 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
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
- 4. A cistern can be filled by two pipes in 30 and 40 minutes respectively. Both the pipes were opened at once, but after some time the first was shut up and the cistern was filled in 10 minutes more. How long after the pipes had opened was the first pipe shut up?
Options- A. 90/ 11 minutes
- B. 90/7 minutes
- C. 90/13 minutes
- D. 45/2 minute Discuss
Correct Answer: 90/7 minutes
Explanation:
Let the first pipe be shut up after x minutes
Now, applying the given rule, we have 30{1 - (x + 10)/40 } = x
[Here t = (x + 10) minutes]
or x = 90/7 minutes
- 5. A cistern has a leak which would empty it in 15 hours. A tap is turned on which admits 2 litres per hour into the cistern and it is now emptied in 10 hours. How many litres does the cistern hold?
Options- A. 50 litres
- B. 60 litres
- C. 45 litres
- D. 360 litres Discuss
Correct Answer: 60 litres
Explanation:
Here w = 2 litres per hour
? Required answer = {(15 x 10) / (15 - 10)} x 2 = 60 litres.
- 6. There are two tank A and B to fill up a water tank. The tank can be filled in 40 min, if both taps are on. The same tank can be filled in 60 min, if tap A alone is on. How much time will tap B alone take, to fill up the same tank?
Options- A. 64 min
- B. 80 min
- C. 96 min
- D. 120 min Discuss
Correct Answer: 120 min
Explanation:
Part filled by tap A in 1 min = 1/60
Let tap B fills the tank in x min
Then, Part filled by tap, B in 1 min = 1/x
According to the question,
1/60 + 1/x = 1/40
? 1/x = 1/40 - 1/60
&rArr ; 1/x = (3 - 2)/120
&rArr ; 1/x = 1/120
? Tap B can fill the tank in 120 min.
- 7. Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in 3 and 4 h, respectively. The full cistern is emptied by the third tap in 5 h. If all three taps are opened simultaneously, the empty cistern will be filled up in?
Options- A. 114/23 h
- B. 214/23 h
- C. 2 h 40 min
- D. 1 h 56 min Discuss
Correct Answer: 214/23 h
Explanation:
Part of tank filled by first tap in 1 h = 1/3
Part of tank filled by second tap in 1 h = 1/4
Part of tank emptied by third tap in 1 h = 1/5
Part of the tank filled by all pipes opened simultaneously in 1 h
= 1/3 + 1/4 - 1/5 = (20 + 15 - 12)/60 = 23/60
Time taken by all the taps to fill the tank when it is empty = 23/60 h = 214/23 h
- 8. Pipe A can fill a Tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full?
Options- A. 93/13 h
- B. 94/13 h
- C. 97/13 h
- D. 99/13 h Discuss
Correct Answer: 93/13 h
Explanation:
Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/10
Part emptied by C in 1 min = - 1/40
Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 )
= (4 + 12 - 3)/120 = 13/120
? Required time to fill the tank = 120/13 = 93/13 h
- 9. Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?
Options- A. 16 h
- B. 20 h
- C. 32 h
- D. 40 h Discuss
Correct Answer: 40 h
Explanation:
Let the leak takes x h to empty the tank.
Now, part filled by inlet in 1 h = 1/8
part filled in 1 h when both tap and leak works together = 1/(8+2) = 1/10
According to the question.
1/x = 1/8 - 1/10 = (5 - 4) / 40 = 1/40
? x = 40 h
- 10. Two pipes A and B can fill a tank in 1 h and 75 min, respectively. There is also an outlet C . If all the three pipes are opened together. The tank is full 50 min. How much time will be taken by C to empty the full tank?
Options- A. 100 min
- B. 150 min
- C. 200 min
- D. 125 min Discuss
Correct Answer: 100 min
Explanation:
Work done by C in 1 min = (1/60 + 1/75 - 1/50 )
= (5 + 4 - 6)/300 = 3/300 = 1/100
Hence, C can empty the full tank in 100 min.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.