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  • Question
  • M, N and O can complete the work in 18, 36 and 54 days respectively. M started the work and worked for 8 days, then N and O joined him and they all worked together for some days. M left the job one day before completion of work. For how many days they all worked together?


  • Options
  • A. 4
  • B. 5
  • C. 3
  • D. 6

  • Correct Answer


  • Explanation

    Let M, N and O worked together for x days.

    From the given data,
    M alone worked for 8 days
    M,N,O worked for x days
    N, O worked for 1 day

    But given that
    M alone can complete the work in 18 days
    N alone can complete the work in 36 days
    O alone can complete the work in 54 days

    The total work can be the LCM of 18, 6, 54 = 108 units

    M's 1 day work = 108/18 = 6 units
    N's 1 day work = 108/36 = 3 units
    O's 1 day work = 108/54 = 2 units

    Now, the equation is
    8 x 6 + 11x + 5 x 1 = 108
    48 + 11x + 5 = 108
    11x = 103 - 48
    11x = 55
    x = 5 days.

    Hence, all M,N and O together worked for 5 days.

  • Tags: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO

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