Pipes and Cistern problems
- 1. Inlet A is four times faster than inlet B to fill a tank. If A alone can fill it in 15 min, how long will it take if both the pipes are opened together?
Options- A. 10 min
- B. 12 min
- C. 15 min
- D. 14 min Discuss
Correct Answer: 12 min
Explanation:
Time taken by A to fill the tank, m = 15 min
? Time taken by B to fill the tank, n = 15 x 4 = 60
? Required time taken m x n/(m + n)
= (15 x 60)/(15 + 60) = (15 x 60)/75 = 12 min
- 2. There are two inlets A and B connected to a tank. A and B can fill the tank in 16 h and 10 h, respectively. If both the pipes are opened alternately for 1 h, starting from A, then how much time will the tank take to filled?
Options- A. 131/4 h
- B. 116/8 h
- C. 122/5 h
- D. 121/4 h Discuss
Correct Answer: 122/5 h
Explanation:
Part filled by A in 1 h = 1/16
Part fill by B in 1 h = 1/10
Part filled by ( A + B ) in 2 h = 1/16 + 1/10 = 13/80
? Part filled by ( A + B ) in 12 h = 6 x 13/80 = 78/80
? Remaining part = 1 - 78/80 = 2/80 = 1/40
Now, it is the turn of A
Time taken by A to fill 1/40 part of the tank = (1/40) x 16 = 2/5 h
? Total time taken ( 12 + 2/5) h = 122/5 h
- 3. Two pipes X and Y can fill a cistern in 6 and 7 min, respectively. Starting with pipe X, both the pipes are opened alternately, each for 1 min. In what time will they fill the cistern?
Options- A. 62/7 min
- B. 63/7 min
- C. 65/7 min
- D. 61/7 min Discuss
Correct Answer: 63/7 min
Explanation:
Part filled by X in 1st min and Y in the 2nd min = ( 1/6 + 1/7) = 13/42
Part filled by ( X + Y ) working alternately in 6 min = 1/2 x 13/42 x 6 =13/14
? Remaining Part = ( 1- 13/14 ) = 1/14
Now, it is the turn of X, one-sixth part is filled in 1 min.
One-fourteenth part is filled in (6 x 1/14) min = 3/7
? Required time = ( 6 + 3/7 ) = 63/7 min
- 4. A tap having diameter 'd' empty a tank in 40 min. How long another tap having diameter '2d' take to empty the same tank?
Options- A. 5 min
- B. 20 min
- C. 10 min
- D. 80 min Discuss
Correct Answer: 20 min
Explanation:
Area of tap ? Work done by pipe.
When diameter is doubled, area will be four times. so, it will work four times faster.
Hence, required time taken to empty the tank = 40 x 1/4 = 10 min.
- 5. Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed so that the tank is full in 9 min?
Options- A. 40 min
- B. 30 min
- C. 10 min
- D. 20 min Discuss
Correct Answer: 20 min
Explanation:
Here, A = 24 min, B = 32, T = 9 min
? Required time = B(1 - T/A )
= 32 ( 1 - 9/24 )
= 32 x 15/24 = 20 min.
- 6. A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open 5 min in the beginning and then the third pipe is also opened.Time taken to empty the cistern is?
Options- A. 38 min
- B. 22 min
- C. 42 min
- D. 45 min Discuss
Correct Answer: 45 min
Explanation:
Let the number of minutes taken to empty the cistern be T min.
According to the questions,
T/6 - (T + 5)/12 - (T + 5)/15 = 0
? T/6 - T/12 - 5/12 - T/12 - T/12 - T/15 = 0
? T/6 - T/12 - T/15 = 5/12 + 5/15
? (10T - 5T - 4T)/ 60 = (25 + 20)/60
? T/60 = 45/60
? T = 45 min.
- 7. A tank be filled by one tap in 20 min. and by another in 25 min. Both the taps are kept open for 5 min. and then the second is turned off. In how many minutes more is the tank completely filled?
Options- A. 171/2 min.
- B. 12 min.
- C. 11 min.
- D. 6 min. Discuss
Correct Answer: 11 min.
Explanation:
Work done by both the taps in 5 min
= 5 (1/20 +1/25) = (5 x 9)/100 = 9/20
Remaining part = (1 - 9/20) = 11/20
Now, 1/20 part is filled in 1 min.
So, 11/20 part will be filled in 11 min.
Hence, the tank will be full in 11 more min.
- 8. A cistern has two taps which fill it in 12 min. and 15 min. respectively. There is also a waste pipe in the cistern. When all the pipes are opened the empty cistern is full in 20 min. how long will the waste pipe take to empty a full cistern?
Options- A. 8 min.
- B. 10 min.
- C. 12 min.
- D. 16 min. Discuss
Correct Answer: 10 min.
Explanation:
Work done by waste pipe in 1 min. = (1/12 + 1/15) - 1/20
= (3/20 - 1/20) = 1/10
? Waste pipe can empty the cistern in 10 min.
- 9. Two taps can separately fill a cistern in 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options- A. 7 minutes
- B. 9 minutes
- C. 13 minutes
- D. 23 minutes Discuss
Correct Answer: 9 minutes
Explanation:
Work done by waste pipe in 1 min. = (1/10) + (1/15) - (1/18)
= (1/6) - (1/18) = 1/9
? Waste pipe can empty the cistern in 9 min.
- 10. A tank is filled by a pipe A in 32 minutes and pipe B in 36 minutes. When full, it in can be emptied by a pipe C in 20 minutes. If all the three pipes are opened simultaneously, half of the tank will be filled in?
Options- A. 16 minutes
- B. 24 minutes
- C. 48 minutes
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Net filling in 1 min. = (1/32 + 1/36 - 1/20) = 13/1440
? Time taken to fill the tank = (1440/13) min.
Time taken to fill half of the tank = (1440/13) x 2 min. = (720/13) min.
= 555/13 min.
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