Pipes and Cistern


  1. Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank?









  1. View Hint View Answer Discuss in Forum

    Part of the tank filled in 1 min by A, B and C = 1/20 + 1/15 +1/12
    = (3 + 4 + 5)/60 = 12/60 = 1/5
    ∴ Time taken by A, B and C to fill the tank = 5 min

    Correct Option: B

    Part of the tank filled in 1 min by A, B and C = 1/20 + 1/15 +1/12
    = (3 + 4 + 5)/60 = 12/60 = 1/5
    ∴ Time taken by A, B and C to fill the tank = 5 min
    ∴ Time taken by A, B and C to fill 40% of the tank = 40% of 5 = (40/100) x 5 = 2 min.


  1. Capacity of tap B is 80% more than that of A. If both the taps are opened simultaneously, they take 45 h to fill the tank. How long will B take to fill the tank alone?









  1. View Hint View Answer Discuss in Forum

    Let time taken by B to fill the tank = T h.
    ∴ Time taken by A to fill the tank = T + (T x 80)/100 = 9T/5 h

    According to the formula,
    Time taken by both the taps to fill the tank = ab /(a + b)

    Correct Option: D

    Let time taken by B to fill the tank = T h.
    ∴ Time taken by A to fill the tank = T + (T x 80)/100 = 9T/5 h

    According to the formula,
    Time taken by both the taps to fill the tank = ab /(a + b)
    ⇒ 45 = (T x 9T/5)/(T + 9T/5)
    ⇒ 45 x 14T/5 = 9T2/5
    ∴ T = 45 x 14/9 = 70 h



  1. Taps A, B and C are attached with a tank and velocity of water coming through them are 42 L/h, 56 L/h and 48 L/h, respectively. A and B are inlets and C is outlet. If all the taps are opened simultaneously, tank is filled in 16 h. What is the capacity of the tank?









  1. View Hint View Answer Discuss in Forum

    Quantity of water admitted by tap A in 1 h = 42 L
    Quantity of water admitted by tap B in 1h = 56 L
    Quantity of water removed by tap C in 1 h = 48 L
    So, quantity of water filled in the tank in 1 h = ( 42 + 56 - 48 ) L = 50 L

    Correct Option: C

    Quantity of water admitted by tap A in 1 h = 42 L
    Quantity of water admitted by tap B in 1h = 56 L
    Quantity of water removed by tap C in 1 h = 48 L
    So, quantity of water filled in the tank in 1 h = ( 42 + 56 - 48 ) L = 50 L
    ∴ Quantity for water filled in 16 h = 16 x 50 = 800 L
    Hence, capacity of tank = 800 L


  1. Two taps A and B can fill a tank in 25 min and 20 min, respectively. But taps are not opened properly so the taps A and B allow 5/6th and 2/3rd part of water, respectively. How long will they take to fill the tank?









  1. View Hint View Answer Discuss in Forum

    Part of the tank filled with A and B in
    1 min = 1/25 x 5/6 + 1/20 x 2/3 = 1/30 + 1/30
    = 2/30 = 1/15

    Correct Option: A

    Part of the tank filled with A and B in
    1 min = 1/25 x 5/6 + 1/20 x 2/3 = 1/30 + 1/30
    = 2/30 = 1/15
    Hence, Time taken to fill the tank = 15 min



  1. Two taps A and B can fill a tank in 20 min and 30 min, respectively. An outlet pipe C can empty the full tank in 15 min. A, B and C are opened alternatively, each for 1 min. How long will the tank take to be filled?









  1. View Hint View Answer Discuss in Forum

    Part of the tank filled by the taps A, B and C in 3 min = 1/20 + 1/30 - 1/15 = (3 + 2 - 4)/60 = 1/60
    ∴ Time taken to fill [ 1 - ( 1/20 + 1/30 )] or 55/60th part of the tank = 3 x 55 = 165 min
    Remaining part of the tank = 1 - 55/60 = 5/60 = 1/12
    Tap A fill 1/0 part in 1 min, then
    Remaining part = 1/12 - 1/20 = (5 -3)/60 = 2/60 = 1/30
    i.e, 1/30th part is filled by B in 1 min
    Hence, required time to fill the whole tank = (165 + 1 +1 ) min = 167 min

    Correct Option: C

    Part of the tank filled by the taps A, B and C in 3 min = 1/20 + 1/30 - 1/15 = (3 + 2 - 4)/60 = 1/60
    ∴ Time taken to fill [ 1 - ( 1/20 + 1/30 )] or 55/60th part of the tank = 3 x 55 = 165 min
    Remaining part of the tank = 1 - 55/60 = 5/60 = 1/12
    Tap A fill 1/0 part in 1 min, then
    Remaining part = 1/12 - 1/20 = (5 -3)/60 = 2/60 = 1/30
    i.e, 1/30th part is filled by B in 1 min
    Hence, required time to fill the whole tank = (165 + 1 +1 ) min = 167 min