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- Question
- Pipe A fills the cistern in half an hour and pipe B in 40 minutes, but owing to a crack in the bottom of the cistern it is found that pipe A now takes, 40 minutes to fill the cistern. How long will B take now to fill it and how long will the crack take to empty it?
Options- A. The leak empties in 1 hour and B fills in 2 hours
- B. B fills in an hour and the leak empties in 2 hours
- C. B fills in an hour and the leak empties in an hour
- D. Data inadequate
- Correct Answer
- B fills in an hour and the leak empties in 2 hours
ExplanationLet the leak empties it in T hours
From the given rule, we have (T x 30) / (T - 30) = 40
? T = 120 minutes = 2 hours.
Now, from the question, applying the rule, we have time taken by B to fill the tank when crack in the bottom develops
= (120 x 40) / (120 - 40) = 60 minutes = 1 hour - 1. A cistern can be filled by one of two pipes in 30 minutes and by the other in 36 minutes. Both pipes are opened together for a certain time but being particularly clogged only 5 / 6 of the full quantity of water flows through the former and only 9 / 10 through the later. The obstructions, however, being suddenly removed the cistern is filled in 15 1/ 2 minutes from that moment. How long was it before the full flow of water began?
Options- A. 1 minutes
- B. 2 minutes
- C. 21/2 minutes
- D. 11/2 minutes Discuss
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. A and B are 20 km apart. A can walk at an average speed of 4 km/hr and B at 6 km/h. If they start walking towards each other at 7:000 am, when they will meet?
Options- A. 8:00 am
- B. 8:30 am
- C. 9:00 am
- D. 10:00 am Discuss
- 7. Arjun runs a distance of 1500 m in 5 minutes. What is his speed in Km/hr?
Options- A. 16 km/hr
- B. 18 km/hr
- C. 15 km/hr
- D. 20 km/hr Discuss
- 8. In how many minutes will Rohit cover a distance of 800 m, if he runs at speed of 10 km/hr?
Options- A. 5 min 12 sec
- B. 4 min 40 sec
- C. 5 min
- D. 4 min 48 sec Discuss
- 9. A plane flies along the four sides of a square field at a speed of 200, 400, 600 and 800 km/hr. Then find the average speed of plane around the square field.
Options- A. 394
- B. 400
- C. 414
- D. 384 Discuss
- 10. Laxman has to cover a distance of 6 km in 45 minutes . If he cover one half of the distance in 2/3 rd time . what should be his speed to cover the remaining distance in the remaining time?
Options- A. 12 km/hr.
- B. 16 km/hr.
- C. 3 km/hr.
- D. 8 km/hr. Discuss
Pipes and Cistern problems
Search Results
Correct Answer: 1 minutes
Explanation:
Net filling in last 151/2 minutes
= 31/2 (1/30 + 1/36) = 341/360
Now, suppose they remained clogged for x minutes.
Net filling in these x minutes
= (x/30 x 5/6 + x/36 x 9/10) = 19 x/360
Remaining part = (1 - 19x/360) = (360 - 19x/360)
360 - 19x/360 = 341/360 or x = 1.
Hence, the pipes remained clogged for 1 minutes.
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.
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
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
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.
Correct Answer: 9:00 am
Explanation:
Suppose they will meet after T hours.
Distance = Speed x Time
Sum of distance traveled by them after T hours
6T + 4T = 20 km
T = 2 hours.
So they will meet at 7:00 AM + 2 hours = 9:00 AM
Correct Answer: 18 km/hr
Explanation:
Speed = (1500/300 ) m/sec
= 5 m/sec
= (5 x 18/5 ) km/hr
= 18 km/hr
Correct Answer: 4 min 48 sec
Explanation:
Rohit's speed = 10 Km/hr = (10 x 5/18) m/sec = 50/18 m/sec
Time taken to cover 800 m = (800 / (50/18) ) sec
= (800 x 18/50) sec = 288 sec = 4 min 48 sec
Correct Answer: 384
Explanation:
Let the side of the square field be x and the average speed of plane be y
x/200 + x/400 + x/600 + x/800 = 4x/y
? 25x/2400 = 4x/y
? y =384
? Average speed is 384 km/hr
Correct Answer: 3 km/hr.
Explanation:
? Time left = (1/3 X 45/60) hr.
= 1/4 hr.
Distance left = 3km
? speed required = [3 / (1/4) ] km/hr.
= 3 x 4
=12km/hr .
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