Pipes and Cistern
 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 ?

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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
 An outlet pipe can empty a cistern in 3 h. In what time will the pipe empty twothird part of the cistern?

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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 hCorrect 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
 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 ?

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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 = 1/40Correct 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.
 If a pipe fills a tank in 6 h, then what part of the tank will the pipe fill in 1 h ?

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

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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