Pipes and Cistern

Pipes and Cistern

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Aptitude miscellaneous
  1. Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank.








  1. View Hint View Answer Discuss in Forum

    Part filled by 1st pipe in 1 min = 1/20
    Part filled by 2nd pipe in 1 min = 1/24
    Part filled by all the pipes in 1 min = 1/15
    Work done by the waste pipe 1 min
    = 1/15 - (1/20 + 1/24 )
    = 1/15 - 11/120
    = (8 - 11)/120 = ( - 3/120 ) = ( -1/40 )

    Correct Option: D

    Part filled by 1st pipe in 1 min = 1/20
    Part filled by 2nd pipe in 1 min = 1/24
    Part filled by all the pipes in 1 min = 1/15
    Work done by the waste pipe 1 min
    = 1/15 - (1/20 + 1/24 )
    = 1/15 - 11/120
    = (8 - 11)/120 = ( - 3/120 ) = ( -1/40 )
    [-ve sign indicates emptying]
    Now, volume of 1/40 part = 6 gallon
    ∴ Volume of whole tank = 40 x 6 = 240 gallon

  1. There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank.








  1. View Hint View Answer Discuss in Forum

    1st pipe takes 1 h to fill 1/2 part of the tank.
    So, time taken to fill the whole tank (m) = 2 h
    2nd pipe takes 1 h to 1/3 part of the tank
    So, time taken to fill the whole tank (n) = 3 h
    Let 3rd pipe takes P h to empty the tank = x
    ∴ 1/m + 1/n - 1/x = 7/12 ⇒ 1/2 + 1/3 - 1/x = 7/12
    ⇒ 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4

    Correct Option: B

    1st pipe takes 1 h to fill 1/2 part of the tank.
    So, time taken to fill the whole tank (m) = 2 h
    2nd pipe takes 1 h to 1/3 part of the tank
    So, time taken to fill the whole tank (n) = 3 h
    Let 3rd pipe takes P h to empty the tank = x
    ∴ 1/m + 1/n - 1/x = 7/12 ⇒ 1/2 + 1/3 - 1/x = 7/12
    ⇒ 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4
    ∴ x = 4 h

  1. Two pipes A and B are opened together to fill a tank. Both pipes fill the tank in a certain time. If A separately takes 16 min more than the time taken by ( A + B ) and B takes 9 min more than the time taken by ( A + B ). Find the time taken by A and B to fill the tank when both the pipes are opened together.








  1. View Hint View Answer Discuss in Forum

    Here, a = 16 and = 9
    Required time = √ab

    Correct Option: B

    Here, a = 16 and = 9
    Required time = √ab
    √16 x 9 = 4 x 3 = 12 min

  1. Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?








  1. View Hint View Answer Discuss in Forum

    Part filled by pipe P in 1 min = 1/12
    Part filled by pipe Q in 1 min = 1/15
    Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
    Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
    ∴ Remaining part = 1 - 9/20 = 11/20

    Correct Option: A

    Part filled by pipe P in 1 min = 1/12
    Part filled by pipe Q in 1 min = 1/15
    Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
    Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
    ∴ Remaining part = 1 - 9/20 = 11/20
    Let the remaining part is filled by pipe Q in T min.
    Then, T/15 = 11/20
    T = (15 x 11)/20 = (3 x 11)/4
    = 33/4 = 84/4 min

  1. A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. in how much time A, B and C fill up the tank together?








  1. View Hint View Answer Discuss in Forum

    Part filled by ( A + B ) in 1 h = 1/6
    Part filled by ( B + C ) in 1 h = 1/10
    Part filled by ( A + C ) in 1 h = 1/12
    ∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
    ∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40

    Correct Option: D

    Part filled by ( A + B ) in 1 h = 1/6
    Part filled by ( B + C ) in 1 h = 1/10
    Part filled by ( A + C ) in 1 h = 1/12
    ∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
    ∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40
    ∴ Required time 40/7 = 55/7 h