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Discussion :: Time and Work

  1. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
    2. A.

    23 days
    B.

    37 days
    C.

    37\(\frac { 1 } { 2 } \)
    D.

    40 days

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    Workspace

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    Answer : Option C

    Explanation :

    Whole work is done by A in[\([20*\frac { 5 } {4 } ]\)= 25 days.

     

    Now,[1-\(\frac { 4 } { 5 } \)]i.e.,\(\frac {1 } { 5 } \)work is done by A and B in 3 days

     

    Whole work will be done by A and B in (3 x 5) = 15 days.

     

    A's 1 day's work =\(\frac {1 } { 25 } \),, (A + B)'s 1 day's work =\(\frac {1 } { 15 } \)

     

    Therefore B's 1 day's work =[\(\frac {1 } { 15 } \)-\(\frac {1 } { 25 } \)]=\(\frac {4 } { 150 } \)=\(\frac {2 } { 75 } \)

     

    So, B alone would do the work in\(\frac {75 } { 2 } \)=37\( \frac { 1 } { 2 } \)days

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