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    A can lay railway tracks between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days on
    Question

    A can lay railway tracks between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Considering this, C alone can do the job in:

    A.

    548\tfrac{5}{48} days​

    B.

    165\tfrac{16}{5}​ days

    C.

    48 days

    D.

    485\tfrac{48}{5}​ days

    Correct option is D

    Given:

    A can complete the work in 16 days.

    B can complete the work in 12 days.

    A, B, and C together complete the work in 4 days.

    Formula Used:

    Work done per day=1Total days taken\text{Work done per day} = \frac{1}{\text{Total days taken}}​​

    Efficiency of C=Total efficiency(Efficiency of A+Efficiency of B)\text{Efficiency of C} = \text{Total efficiency} - (\text{Efficiency of A} + \text{Efficiency of B})​​

    Solution:

    Work done by A in 1 day = 116\frac{1}{16}​​

    Work done by B in 1 day =112 \frac{1}{12}​​

    Work done by A, B, and C together in 1 day =14 \frac{1}{4}​​​

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

    1C=14116112=123448=548\frac{1}{C} = \frac{1}{4} - \frac{1}{16} - \frac{1}{12} = \frac{12-3-4}{48}=\frac{5}{48}​​

    C=485\frac{48}{5} days

    Option (D) is right.

    Alternate Method:

    ​Efficiency of C= 12 - 4 - 3 = 5

    Time taken by C=485\frac{48}{5} days

    Option (D) is right.​

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