Pipes and Cistern


  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. 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 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. A tank can be filled by a tap in 20 min and by another tap in 60 min. Both the taps are kept open for 5 min and then the 1st tap is shut off. After this, how much time the tank will be completely filled?









  1. View Hint View Answer Discuss in Forum

    Part of the tank filled by both taps in 5 min = 5 x (1/20 + 1/60)
    = 5 x (6 +2 )/120 = 8/24 = 1/3
    ∴ Remaining part = (1 - 1/3) = 2/3
    ∵ 1/60 Part is now filled in 1 min.

    Correct Option: D

    Part of the tank filled by both taps in 5 min = 5 x (1/20 + 1/60)
    = 5 x (6 +2 )/120 = 8/24 = 1/3
    ∴ Remaining part = (1 - 1/3) = 2/3
    ∵ 1/60 Part is now filled in 1 min.
    ∴ 2/3 Part is now filled in 60 x 2/3 = 40 min.



  1. A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively , at what time will the cistern be empty?









  1. View Hint View Answer Discuss in Forum

    Let the cistern gets emptied in m h after 3:pm
    Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0

    Correct Option: B

    Let the cistern gets emptied in m h after 3:pm
    Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0
    ⇒ m/3 + (m - 1)/4 - (m - 2) = 0
    ⇒ 4m + 3(m - 1) - 12(m - 2) = 0
    ⇒ 5m = 21
    ⇒ m = 21/5 = 4.2
    ∴ m = 4 h 12 min
    ∵ Required time = 7 : 12 pm.