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SSC Quantitative Aptitude Pipes & Cisterns Question Bank Pipe and Cistern (II)

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

    A) 6 : 15pm

    B) 7 : 12pm

    C) 8 : 12pm

    D) 8 : 35pm

    Correct Answer: B

    Solution :

    [b] Let the cistern be emptied in x h after 3 pm Work done by A in x h, by B in \[(x-1)\,h\]and by C in \[(x-3)\,h=0\] \[\Rightarrow \] \[\frac{x}{3}+\frac{x-1}{4}-(x-2)=0\] \[\Rightarrow \] \[4x+3\,(x-1)-12\,(x-2)=0\] \[\Rightarrow \] \[5x=21\] \[\Rightarrow \] \[x=4\,h\,12\min \] Required time is 7 : 12 pm.


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