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Discussion :: Time and Work

  1. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

    2. A.

    13\( \frac { 1 } { 3 } \)days
    B.

    15 days
    C.

    20 days
    D.

    26 days

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    Workspace

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    Answer : Option A

    Explanation :

    Work done by X in 8 days =\( [\frac { 1 } { 40 } *8]\)=\( \frac { 1 } { 5 } \)

     

    Remaining work =[1-\( \frac { 1 } { 5 } \)]=\( \frac { 4 } { 5 } \)

     

    Now,\( \frac { 4 } { 5 } \)work is done by Y in 16 days.

     

    Whole work will be done by Y in\( [16*\frac { 5} {4 } ]\)=20 days.

     

    ThereforeX's 1 day's work =\(\frac { 1 } { 40} \)Y's 1 day's work =\(\frac { 1 } { 20} \)

     

    (X + Y)'s 1 day's work =[\(\frac { 1 } { 40} \)+\(\frac { 1 } { 20} \)]=\(\frac { 3 } { 40} \)

     

    Hence, X and Y will together complete the work in\(( \frac { 40 } {3 } )\)=13\( \frac { 1 } { 3 } \)days

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