## Pipes and Cistern

#### Pipes and Cistern

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 ?

1. When a pipe fills 1/m part of a tank in 1 h, then the pipe takes m h to fill the tank.

##### Correct Option: D

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

1. An outlet pipe can empty a cistern in 3 h. In what time will the pipe empty two-third part of the cistern?

1. 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

##### Correct Option: B

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

1. 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 ?

1. 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

##### Correct Option: A

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.

1. If a pipe fills a tank in 6 h, then what part of the tank will the pipe fill in 1 h ?

1. We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m

##### Correct Option: B

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

1. An outlet pipe can empty a cistern in 30 min, then what part of the cistern will it empty in 1 min ?

1. We know that, when a pipe empties a cistern in n min, then the part emptied by the pipe in 1 min = 1/n

##### Correct Option: C

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