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    MI alone can do a work in 14 days and M2 alone can do the same work in 70 days. With help of M3, they finish the same work in 7 days. In how many days
    Question

    MI alone can do a work in 14 days and M2 alone can do the same work in 70 days. With help of M3, they finish the same work in 7 days. In how many days M3 alone can do the same work?

    A.

    20 days

    B.

    17.5 days

    C.

    19 days

    D.

    21 days

    Correct option is B

    Given: MI alone: 14 days, M2 alone: 70 days, M1 + M2 + M3 together: 7 days
    Formula Used: Work done per day = 1/Days for each worker
    Solution:

    Work done by M1 in 1 day = 1/14,

    M2 in 1 day = 1/70,

    M1 + M2 + M3 in 1 day = 1/7
    Let work done by M3 in 1 day = 1/M3 days
    114+170+1M3=17570+170+1M3=17670+1M3=171M3=176701M3=10706701M3=4701M3=235M3=352=17.5days\begin{aligned}&\frac{1}{14} + \frac{1}{70} + \frac{1}{M_3} = \frac{1}{7} \\&\frac{5}{70} + \frac{1}{70} + \frac{1}{M_3} = \frac{1}{7} \\&\frac{6}{70} + \frac{1}{M_3} = \frac{1}{7} \\&\frac{1}{M_3} = \frac{1}{7} - \frac{6}{70} \\&\frac{1}{M_3} = \frac{10}{70} - \frac{6}{70} \\&\frac{1}{M_3} = \frac{4}{70} \\&\frac{1}{M_3} = \frac{2}{35} \\&M_3 = \frac{35}{2}= 17.5 days\end{aligned}​​

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