## Pipes and Cistern

#### Pipes and Cistern

1. 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 ?

1. 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

##### Correct Option: D

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

1. 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 ?

1. Part emptied in 1 min. = (1/8 - 1/16) = 1/16
∴ Time taken to empty the full tank = 16 min.

##### Correct Option: D

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.

1. 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 ?

1. Net filling in 1 hour = (1/4 + 1/6 - 1/8) = 7/24

##### Correct Option: B

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.

1. 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 ?

1. Net filling in 1 hour = (1/2 - 1/3) = 1/6

##### Correct Option: B

Net filling in 1 hour = (1/2 - 1/3) = 1/6
∴ Time taken to fill the cistern = 6 hours

1. 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) ?

1. Net filling in 1 hour = (1/x - 1/y) = (y - x) / xy

##### Correct Option: D

Net filling in 1 hour = (1/x - 1/y) = (y - x) / xy
∴ Time taken to fill the tank = xy / (y - x) hrs.