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Pipe & Cisterns Test 391
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Pipe & Cisterns Test 391

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  • Question 1/10
    1 / -0.25
    Two pipes, P and Q can fill a cistern in 15 and 18 minutes respectively. If both are opened together and at the end of 3 minutes, Q is closed, how much longer will the cistern take to fill?
    Solutions
    Let the total time taken by the pipes be t.
    Pipe P fills the cistern in 15 minutes
    So, in 1 minute, Pipe P will fill = 1/15 part of cistern
    In 3 minutes, pipe P will fill (1/15) × 3 = 1/5 part of cistern
    Similarly, Pipe Q will fill 3/18 = 1/6 part of cistern.
    So collectively in the first three minutes both the pipes will fill 1/5 + 1/6 = 11/30 part of the cistern and then Q was closed.
    The remaining part 1− 11/30 =19/30 part of the cistern is needed to be filled by P.
    Since, time taken by P to fill 1 cistern = 15 minutes
    Time taken by P to fill 19/30 of the cistern = 15 ×19/30 = 9.5 minutes
    So, P takes 9.5 more minutes to fill the cistern.
  • Question 2/10
    1 / -0.25
    Pipes A and B can fill an empty tank in 4 and 6 hrs respectively. If they are opened on alternate hours starting with A, then in how many hours the tank shall be full?
    Solutions
    Capacity of tank

    Capacity of the tank filled in 2 hrs
    10 units will be filled in hrs.
    Rest capacity
    2 units will be filled by A in 2/3 hrs.
    Total time     hrs
  • Question 3/10
    1 / -0.25
    12 pumps working 6 hrs a day can empty a completely filled reservoir in 15 days. How many such pumps working 9 hrs a day will empty the same reservoir in 12 days?
    Solutions
    Given that,
     
    N1 = 12, T1 = 6 hrs, D1 = 15 days, 

    and N2 = ?, T2 = 9 hrs, D2 = 12 days

    Now, N1.T1.D1 = N2.T2.D2 
     
    = 12 x 6 x 15 = N2 x 9 x 12 

    = N2 = 10  
  • Question 4/10
    1 / -0.25
    Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
    Solutions
    Let B be turned off after x minutes. Then,
    Part filled by (A + B) in x min + Part filled by A in (30 - x) min = 1
    ∴ x(2/75 + 1/45) + (30 - x)*(2/75) = 1

    ⇒ x/45 + 4/5 = 1

    ⇒ x/45 = 1/5

    ⇒ x = 9 min.
  • Question 5/10
    1 / -0.25
    An inlet pipe can fill a water tank in 2 hours. There is a leak in the bottom of tank, and hence it took 2 hours 45 min to fill the tank. The leak can drain all the water of the tank in:
    Solutions
    Capacity of tank units

    Time taken by outlet pipe to empty the tank hrs
  • Question 6/10
    1 / -0.25
    Pipes A, B and C can fill a tank in 10, 15 and 30 hours, respectively. D is an emptying pipe which alone can empty the full tank in x hours. A, B and C are opened together for 3 hours and then closed. Now D is opened which alone empties the tank in 30 hours. What is the value of x?
    Solutions

    Let total capacity of tank = 30 liter (LCM of 10,15,30)

    So, amount of liquid filled by A in an hour = 3 liter

    amount of liquid filled by B in an hour = 2 liter

    amount of liquid filled by C in an hour = 1 liter

    Amount of liquid filled in 3 hrs = 3 x (3+2+1) = 18 liter

    So time taken by D to empty 18/30 liter = 1 hour

    Hence time taken by D to empty 30 liter = 30 ×  = 50 hrs.

  • Question 7/10
    1 / -0.25
    There are 8 pipes in which some are in let and some are outlet pipes. If single inlet pipe fills the tank in 5hrs while single outlet empties the tank in 10 hrs. When all pipes are open simultaneously, they fill the tank 2.5 hrs. Find number of inlet and outlet pipes?
    Solutions
    Let there are x inlet pipes and y outlet pipes, x+y = 8

    A single inlet pipe fills the tank in 1 hr =  1/5

    ∴ x inlet pipe fill tank in 1 hr =  x/5

    Single outlet pipe empty tank in 1 hr =  1/10

    ∴y outlet pipe empty tank in 1 hr = y/10
    Total tank fill when all pipes are opened in 1 hr =
    Time taken to fill tank by all pipes =
    And given,

    2x – y = 4

    And x + y =8

    By solving above equation we get x = 4 and y =4
  • Question 8/10
    1 / -0.25
    A pipe can fill a tank in hrs and another pipe can empty it in hrs If both the pipes are opened in how many hours will the tank be filled?
    Solutions
    Part of the tank filled in 1 hr
    Part of the tank emptied in 1 hr
    Resultant part filled in 1 hr when both pipes are opened
    Tank will be filled in hrs
  • Question 9/10
    1 / -0.25
    Two pipes P and Q can fill acistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes, P is turned off. In how many more minutes will Q fill the cistern?
    Solutions
    Let the capacity of cistern = LCM (12,15) = 60 units

    The capacity of the cistern filled by P and Q together in 3 min = 3x(5+4) = 27 units
    Rest capacity =     60 - 27 = 33 units will be filled by Q alone in min
  • Question 10/10
    1 / -0.25
    A tap can fill a tank in 6 hrs. After half the tank filled, three more similar taps are opened. What is the total time taken to fill the tank?
    Solutions
    Let total capacity of tank
    Efficiency of 1st tank unit/hrs
    Capacity of 1/2 of tank
    Time taken to fill 1/2 of the tank
    3 more taps of capacity 1 unit/hrs are opened with 1st tap.
    Total efficiency     units/hrs
    Time taken to fill the rest of capacity of tank
    Total time
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