Pipes and Cistern problems
- 1. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Options- A.
1 13 hours 17 - B.
2 8 hours 11 - C.
3 9 hours 17 - D.
4 1 hours 2
Discuss
Correct Answer:
| 3 | 9 | hours |
| 17 |
Explanation:
| Net part filled in 1 hour | ❨ | 1 | + | 1 | - | 1 | ❩ | = | 17 | . |
| 5 | 6 | 12 | 60 |
| ∴ The tank will be full in | 60 | hours i.e., 3 | 9 | hours. |
| 17 | 17 |
- 2. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2⅓ hours to fill the tank. The leak can drain all the water of the tank in:
Options- A.
4 1 hours 3 - B. 7 hours
- C. 8 hours
- D. 14 hours Discuss
Correct Answer: 14 hours
Explanation:
| Work done by the leak in 1 hour = | ❨ | 1 | - | 3 | ❩ | = | 1 | . |
| 2 | 7 | 14 |
∴ Leak will empty the tank in 14 hrs.
- 3. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
Options- A. 10 min. 20 sec.
- B. 11 min. 45 sec.
- C. 12 min. 30 sec.
- D. 14 min. 40 sec. Discuss
Correct Answer: 14 min. 40 sec.
Explanation:
| Part filled in 4 minutes = 4 | ❨ | 1 | + | 1 | ❩ | = | 7 | . |
| 15 | 20 | 15 |
| Remaining part = | ❨ | 1 - | 7 | ❩ | = | 8 | . |
| 15 | 15 |
| Part filled by B in 1 minute = | 1 |
| 20 |
| ∴ | 1 | : | 8 | :: 1 : x |
| 20 | 15 |
| x = | ❨ | 8 | x 1 x 20 | ❩ | = 10 | 2 | min = 10 min. 40 sec. |
| 15 | 3 |
∴ The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
- 4. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Options- A. 15 min
- B. 20 min
- C. 27.5 min
- D. 30 min Discuss
Correct Answer: 30 min
Explanation:
| Part filled by (A + B) in 1 minute = | ❨ | 1 | + | 1 | ❩ | = | 1 | . |
| 60 | 40 | 24 |
Suppose the tank is filled in x minutes.
| Then, | x | ❨ | 1 | + | 1 | ❩ | = 1 |
| 2 | 24 | 40 |
| ⟹ | x | x | 1 | = 1 |
| 2 | 15 |
⟹ x = 30 min.
- 5. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Options- A. 81 min.
- B. 108 min.
- C. 144 min.
- D. 192 min. Discuss
Correct Answer: 144 min.
Explanation:
| Then, faster pipe will fill it in | x | minutes. |
| 3 |
| ∴ | 1 | + | 3 | = | 1 |
| x | x | 36 |
| ⟹ | 4 | = | 1 |
| x | 36 |
⟹ x = 144 min.
- 6. Pipe A can fill a tank in 45 hrs and pipe B can fill it in 36 hrs. If both the pipes are opened in the empty tank. In how many hours will it be full?
Options- A. 10 hr
- B. 15 hr
- C. 20 hr
- D. 28 hr Discuss
Correct Answer: 20 hr
Explanation:
Part filled A in 1 hr= (1/45)
Part filled B in 1 hr= (1/36)
Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20
So, The tank will be full in 20 hr.
- 7. If a pipe fills a tank in 6 h, then what part of the tank will the pipe fill in 1 h?
Options- A. 1/3
- B. 1/6
- C. 1/4
- D. 1/5 Discuss
Correct Answer: 1/6
Explanation:
We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m
Here, m = 6
? Required part of the tank to be filled in 1h = 1/6 part
- 8. A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options- A. 16 hrs.
- B. 20 hrs.
- C. 25 hrs.
- D. 40 hrs. Discuss
Correct Answer: 40 hrs.
Explanation:
Work done by leak in 1 hour = (1/8 - 1/10) = 1/40
? The leak will empty the cistern in 40 hours.
- 9. A pipe can empty a tank in 12 minutes and another pipe can empty it in 16 minutes. If both the pipes are opened simultaneously, find the time in which a full tank is emptied?
Options- A. 6 minutes
- B. 61/7 minutes
- C. 62/7 minutes
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Required answer = (12 x 16) /(12 + 16) = 48 / 7 = 66/7 minutes.
- 10. A cistern is normally filled in 8 hrs. but takes 2 hrs. longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options- A. 16 hrs.
- B. 40 hrs.
- C. 25 hrs.
- D. 20 hrs. Discuss
Correct Answer: 40 hrs.
Explanation:
Here x = 8 hrs. and y = 8 + 2 = 10 hrs.
Now, applying the given rule, we have the
Required answer = (8 x 10) /(10 - 8) = 40 hrs.
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