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    Ravi, Arvind and Vimal can complete a piece of work in 5 days, 6 days and 8 days, respectively. In how many days can all the three together compl
    Question

    Ravi, Arvind and Vimal can complete a piece of work in 5 days, 6 days and 8 days, respectively. In how many days can all the three together complete the work?

    A.

    3451 days 3 \dfrac{4}{51} \text{ days} \quad

    B.

    2259 days2 \dfrac{2}{59} \text{ days} \quad​​

    C.

    3665 days3 \dfrac{6}{65} \text{ days} \quad​​

    D.

    2347 days2 \dfrac{3}{47} \text{ days}​​

    Correct option is B

    Given:

    Ravi completes work in 5 days

    Arvind completes work in 6 days

    Vimal completes work in 8 days

    Solution:

    Ravi completes work in 5 days 

    Work rate = 15\frac 15​ per day

    Arvind completes work in 6 days 

    Work rate = 16\frac 16​ per day

    Vimal completes work in 8 days

    Work rate = 18\frac 18 per day

    Total work rate = 15+16+18\frac 15 + \frac16 + \frac18​​

    = 24+20+15120\frac {24+20+15}{120}​​

    =59120\frac {59}{120}​ work per day

    Time = 159120\frac{1}{\frac{59}{120}}​= 12059\frac{120}{59} =22592 \dfrac{2}{59} days

    Alternate Method:

    Total work = 120 unit

    Total efficiency = 24 + 20 + 15 = 59

    Time = 12059\frac{120}{59} =22592 \dfrac{2}{59} days

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