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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?

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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