Pipes and Cistern problems
- 1. A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. in how much time A, B and C fill up the tank together?
Options- A. 9 h
- B. 53/7 h
- C. 52/7 h
- D. 55/7 h Discuss
Correct Answer: 55/7 h
Explanation:
Part filled by ( A + B ) in 1 h = 1/6
Part filled by ( B + C ) in 1 h = 1/10
Part filled by ( A + C ) in 1 h = 1/12
? Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
? Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40
? Required time 40/7 = 55/7 h
- 2. Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?
Options- A. 81/4 min
- B. 83/4 min
- C. 5 min
- D. 81/2 min Discuss
Correct Answer: 81/4 min
Explanation:
Part filled by pipe P in 1 min = 1/12
Part filled by pipe Q in 1 min = 1/15
Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
? Remaining part = 1 - 9/20 = 11/20
Let the remaining part is filled by pipe Q in T min.
Then, T/15 = 11/20
T = (15 x 11)/20 = (3 x 11)/4
= 33/4 = 84/4 min
- 3. Two pipes A and B are opened together to fill a tank. Both pipes fill the tank in a certain time. If A separately takes 16 min more than the time taken by ( A + B ) and B takes 9 min more than the time taken by ( A + B ). Find the time taken by A and B to fill the tank when both the pipes are opened together.
Options- A. 10 min
- B. 12 min
- C. 15 min
- D. 8 min Discuss
Correct Answer: 12 min
Explanation:
Here, a = 16 and = 9
Required time = ?ab
?16 x 9 = 4 x 3 = 12 min
- 4. There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank.
Options- A. 3 h
- B. 4 h
- C. 5 h
- D. 6 h Discuss
Correct Answer: 4 h
Explanation:
1st pipe takes 1 h to fill 1/2 part of the tank.
So, time taken to fill the whole tank (m) = 2 h
2nd pipe takes 1 h to 1/3 part of the tank
So, time taken to fill the whole tank (n) = 3 h
Let 3rd pipe takes P h to empty the tank = x
? 1/m + 1/n - 1/x = 7/12 ? 1/2 + 1/3 - 1/x = 7/12
? 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4
? x = 4 h
- 5. Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank.
Options- A. 210 gallon
- B. 50 gallon
- C. 150 gallon
- D. 240 gallon Discuss
Correct Answer: 240 gallon
Explanation:
Part filled by 1st pipe in 1 min = 1/20
Part filled by 2nd pipe in 1 min = 1/24
Part filled by all the pipes in 1 min = 1/15
Work done by the waste pipe 1 min
= 1/15 - (1/20 + 1/24 )
= 1/15 - 11/120
= (8 - 11)/120 = ( - 3/120 ) = ( -1/40 )
[-ve sign indicates emptying]
Now, volume of 1/40 part = 6 gallon
? Volume of whole tank = 40 x 6 = 240 gallon
- 6. A tank can be filled by a tap in 20 min and by another tap in 60 min. Both the taps are kept open for 5 min and then the 1st tap is shut off. After this, how much time the tank will be completely filled?
Options- A. 20 min
- B. 30 min
- C. 45 min
- D. 40 min Discuss
Correct Answer: 40 min
Explanation:
Part of the tank filled by both taps in 5 min = 5 x (1/20 + 1/60)
= 5 x (6 +2 )/120 = 8/24 = 1/3
? Remaining part = (1 - 1/3) = 2/3
? 1/60 Part is now filled in 1 min.
? 2/3 Part is now filled in 60 x 2/3 = 40 min.
- 7. A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively , at what time will the cistern be empty?
Options- A. 6:15 pm
- B. 7:12 pm
- C. 8:12 pm
- D. 8:35 pm Discuss
Correct Answer: 7:12 pm
Explanation:
Let the cistern gets emptied in m h after 3:pm
Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0
? m/3 + (m - 1)/4 - (m - 2) = 0
? 4m + 3(m - 1) - 12(m - 2) = 0
? 5m = 21
? m = 21/5 = 4.2
? m = 4 h 12 min
? Required time = 7 : 12 pm.
- 8. There are three taps of diameter 1 cm, 4/3 cm and 2 cm, respectively. The ratio of the water flowing through them is equal to the ratio of the square of their diameters. The biggest tap can fill the tank alone in 61 min. If all the taps are opened simultaneously, how long will the tank take to be filled?
Options- A. 44 min
- B. 45 min
- C. 155/18
- D. None of the above Discuss
Correct Answer: None of the above
Explanation:
Time taken to fill the tank by the tap having 2 cm diameter = 61 min
? Time taken to fill the tank by the tap having 1 cm diameter
= 61 x (2/1)2 = 244 min
Similarly, time taken to fill the tank by the tap having 4/3 cm diameter
= 61 x [(2 x 3)/4]2 = 61 x 9/4 = 549/4 min.
? Part of the tank filled by all the three pipes in 1 min
= 1/61 + 1/244 + 1/(549/4)
= (36 + 9 + 16)/2196 = 61/2196 = 1/36
Hence, required time taken = 36 min
- 9. Two pipes can fill a cistern in 14 and 16 h, respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, it took 92 min more to fill the cistern. When the cistern is full, in what time will the leak empty it?
Options- A. 4319/23 h
- B. 4317/23 h
- C. 4313/23 h
- D. 4319/23 h Discuss
Correct Answer: 4319/23 h
Explanation:
Part filled by 1st pipe in 1 h = 1/14
Part filled by 2nd pipe in 1 h = 1/16
Part filled by the two pipes in 1 h
= ( 1/14 + 1/16 ) = (8 + 7)/112 = 15/112
? Time taken by these two pipes to fill the cistern = 112/15 h = 7 h 28 min
Due to leakage, the time taken 7 h 28 min + 92 min = 9 h
&thee4; Work done by ( two pipes + leak ) in 1 h = 1/9
Work done by the leak in 1 h = 1/9 - 15/112 = (112 - 135)/1008
= - 23/1008
? Time taken by leak to empty the full cistern
= 1008/23 = 4319/23 h
- 10. Three taps A,B and C can fill a cistern in 10, 15 and 20 minutes respectively. They are all turned on at once, but after 3 minutes C is turned off. How many minutes longer will A and B take to fill the cistern?
Options- A. 2 min.
- B. 2 min. 6 sec.
- C. 1 min. 6 sec.
- D. 3 min. 8 sec. Discuss
Correct Answer: 2 min. 6 sec.
Explanation:
T = (10 x 15 x 20) / (10 x 15 + 10 x 20 + 15 x 20) = 60/13 minutes
Now, applying the given rule, we have [60/13 x y]/ [y - 60/13 + 3] = 20
or y = 21/10 = 2 min. 6 seconds.
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