## Pipes and Cistern

#### Pipes and Cistern

1. 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 ?

1. Work done by waste pipe in 1 min. = (1/10) + (1/15) - (1/18)

##### Correct Option: B

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.

1. 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 ?

1. 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.

##### Correct Option: C

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.

1. 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 ?

1. Work done by waste pipe in 1 min. = (1/12 + 1/15) - 1/20

##### Correct Option: B

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.

1. 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 ?

1. 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

##### Correct Option: D

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.

1. 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 ?

1. Net filling in 1 min. = (1/32 + 1/36 - 1/20) = 13/1440
∴ Time taken to fill the tank = (1440/13) min.

##### Correct Option: D

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.