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

  • question_answer
    A cistern has 3 pipes A, B and C. A and B call fill it in 3 h and 4 h, respectively and C can empty it in 1 h. If the pipes are opened at 3 pm, 4 pm and 5 pm, respectively on the same day, the cistern will be empty at

    A) 7 : 12 pm

    B) 7 : 15 pm

    C) 7 : 10 pm

    D) 7 : 18 pm

    Correct Answer: A

    Solution :

    [a] Part filled by pipe A in \[2\,h=\frac{2}{3}\] Part filled by pipe B in \[1\,h=\frac{1}{4}\] Total filled part\[=\frac{2}{3}+\frac{1}{4}=\frac{8+3}{12}=\frac{11}{12}\] Now, part emptied by all the three pipes in 1 h \[=1-\frac{1}{3}-\frac{1}{4}=\frac{12-4-3}{12}=\frac{5}{12}\] Since, \[\frac{5}{12}\]part is emptied in 1 h. Therefore, \[\frac{11}{12}\]part is emptied in             \[\frac{11}{12}\times \frac{12}{5}\,h=\frac{11}{5}\,h=2\,h+12\min \] Total required time \[=5\,h+2\,h+12\min =7\,h\,\,12\min \] \[=7:12\,pm.\]


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