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  • Question
  • Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?


  • Options
  • A. 4:18 pm
  • B. 3:09 pm
  • C. 12:15 pm
  • D. 11:09 am

  • Correct Answer
  • 3:09 pm 

    Explanation

    Efficiency of P= 100/20= 5% per hour  

    Efficiency of Q= 100/25= 4% per hour  

    Efficiency of R= 100/40= 2.5% per hour  

    Efficiency of S=100/50= 2% per hour 

     

    Cistern filled till 10 am by P, Q and R  

    Till   10 . 00 am   Pipe   P   filled   20 % Till   10 . 00 am   Pipe   Q   filled   8 % Till   10 . 00 am   Pipe   R   filled   2 . 5 % 30 . 5 %   

    Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern. 

    Rest of cistern to be filled = 100 - 30.5 = 69.5%  

     

    Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern 

    = 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).

    Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins

     

    It means cistern will be filled up at 3:09 pm


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