Pipes and Cistern problems
- 1. An inlet pipe fills 1/8 part of a tank in 1 h. How much time will the pipe take to fill the empty tank?
Options- A. 4 h
- B. 2 h
- C. 6 h
- D. 8 h Discuss
Correct Answer: 8 h
Explanation:
We know that, when a pipe fills 1/m part of a tank in 1 h, then the pipe takes m h to fill the tank.
Here, 1/m = 1/8 ? m = 8
? Required time to fill the tank = 8 h
- 2. An outlet pipe can empty a cistern in 3 h. In what time will the pipe empty two-third part of the cistern?
Options- A. 4 h
- B. 2 h
- C. 3 h
- D. 5 h Discuss
Correct Answer: 2 h
Explanation:
Time taken by the pipe to empty the cistern = 3 h
Then, time taken by the pipe to empty the 2/3 part = 3 x 2/3 = 2 h
- 3. A pipe can fill a tank in 20 h. Due to a leak in the bottom, it is filled in 40 h. If the tank is full, how much time will the leak take to empty it?
Options- A. 40 h
- B. 30 h
- C. 50 h
- D. 30 h Discuss
Correct Answer: 40 h
Explanation:
Let the leak empties the full tank in x h, then
Part emptied in 1 by leak = 1/x
Part filled by inlet in 1 h = 1/20
According to the question,
1/20 + 1/x = 1/40
? 1/x = 1/40 - 1/20 = 1- 2/40 = -1/40 [-ve sign Indicates emptying.]
Clearly, leak will empty the full tank in 40 h.
- 4. 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 1 h = 1/6 part
- 5. An outlet pipe can empty a cistern in 30 min, then what part of the cistern will it empty in 1 min?
Options- A. 1/20
- B. 1/15
- C. 1/30
- D. 1/18 Discuss
Correct Answer: 1/30
Explanation:
We know that, when a pipe empties a cistern in n min, then the part emptied by the pipe in 1 min = 1/n
Here, n=30
? Required part of the tank emptied in 1 min = 1/30 part
- 6. Three pipes A, B and C can fill a tank separately in 8 h,10 h and 20h, respectively. Find the time taken by all the three pipes to fill the tank when these pipes are opened together?
Options- A. 57/11 h
- B. 47/11 h
- C. 87/11 h
- D. 37/11 h Discuss
Correct Answer: 37/11 h
Explanation:
Part filled by A in 1 h = 1/8
Part filled by B in 1 h = 1/10
Part filled by C in 1 h = 1/20
Part filled by (A + B + C) in 1 h = 1/8 + 1/10 + 1/20
= (5 + 4 + 2)/40 = 11/40
? Required time to fill the tank = 40/11 h
= 37/11 h
- 7. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already half full and both the taps are opened together, the tank will be?
Options- A. Filled in 12 min.
- B. Emptied in 12 min.
- C. Filled in 8 min.
- D. Emptied in 8 min. Discuss
Correct Answer: Emptied in 8 min.
Explanation:
Part emptied in 1 min. = (1/8 - 1/16) = 1/16
? Time taken to empty the full tank = 16 min.
Hence, time taken to empty the half tank = 8 min.
- 8. A cistern can be filled by two pipes A and B in 4 hours and 6 hours respectively. When full, the tank can be emptied by a third pipe C in 8 hours . If all the taps be turned on at the same time, the cistern will be full in?
Options- A. 3 hours 18 min.
- B. 3 hours 26 min.
- C. 3 hours 42 min.
- D. 3 hours 48 min. Discuss
Correct Answer: 3 hours 26 min.
Explanation:
Net filling in 1 hour = (1/4 + 1/6 - 1/8) = 7/24
? Time taken to fill the cistern = (24/7) hrs. = 3 hrs. 26 min.
- 9. One tap can fill a cistern in 2 hours and another can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened?
Options- A. 5 hours
- B. 6 hours
- C. 7 hours
- D. 8 hours Discuss
Correct Answer: 6 hours
Explanation:
Net filling in 1 hour = (1/2 - 1/3) = 1/6
? Time taken to fill the cistern = 6 hours
- 10. A pipe can fill a tank in x hours and another can empty it in y hours. They can together fill it in (y > x)?
Options- A. (x - y) hours
- B. (y - x ) hours
- C. xy / (x - y) hours
- D. xy / ( y - x) hours Discuss
Correct Answer: xy / ( y - x) hours
Explanation:
Net filling in 1 hour = (1/x - 1/y) = (y - x) / xy
? Time taken to fill the tank = xy / (y - x) hrs.
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