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    Meenu alone can do a work in 16 days. Simi alone can do it in 12 days. If Raj joins them, they three together can complete the work in 4 days. How lon
    Question

    Meenu alone can do a work in 16 days. Simi alone can do it in 12 days. If Raj joins them, they three together can complete the work in 4 days. How long will Raj alone take to finish the work?

    A.

    1112\frac{111}2​​

    B.

    127\frac{12}7​​

    C.

    485\frac{48}5​​

    D.

    23

    Correct option is C

    Given:
    Meenu can complete the work in 161616 days 




    Simi can complete the work in 121212 days ​112\frac{1}{12}

    All three (Meenu, Simi, and Raj) together can complete the work in 444 days

    Solution:

    Let Raj's work rate = 1R\frac{1}R​ (work per day)  

    Work done by Meenu in one day = 116\frac{1}{16}

    Work done by Simi in one day =  112\frac{1}{12}
    Total work done by all three in one day = 14\frac{1}{4}

    So, their total combined work rate is :

    116+112+1R=14\frac{1}{16}+\frac{1}{12}+\frac{1}{R}=\frac{1}{4}

    348+448+1R=14 \frac{3}{48}+\frac{4}{48}+\frac{1}{R}=\frac{1}{4}​     

    748+1R=14\frac{7}{48}+\frac{1}{R}=\frac{1}{4}​​

    1R=548\frac{1}{R}=\frac{5}{48}​​

    Raj alone will take 485\frac{48}{5} days to complete the work.485\frac{48}{5}​​​​

    14=1248\frac{1}{4} = \frac{12}{48}

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