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Discussion :: Time and Work

  1. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

    2. A.

    18 days
    B.

    24 days
    C.

    30 days
    D.

    36 days

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    Answer : Option A

    Explanation :

    2(A + B + C)'s 1 day's work =[\( \frac { 1 } { 30 } \)+\( \frac { 1 } { 2 4} \)+\( \frac { 1 } { 2 0} ]\)=\( \frac { 1 5} {1 20 }\)=\(\frac { 1 } { 8 }\)

     

    Therefore, (A + B + C)'s 1 day's work =\(\frac { 1 } { 2*8 } \)=\(\frac { 1 } { 16 }\)

     

    Work done by A, B, C in 10 days =\(\frac { 10 } { 16 }\)=\(\frac { 5 } { 8 }\)

     

    Remaining work =[1-\(\frac { 5 } { 8 }\)]=\(\frac { 3 } { 8 }\)

     

    A's 1 day's work =[\(\frac { 1 } { 16 } \)-\(\frac { 1 } { 24 } ]\)=\(\frac { 1 } { 48 }\)

     

    Now,\(\frac { 1 } { 48 }\)work is done by A in 1 day.

     

    So,\(\frac { 3 } { 8 }\)work will be done by A in[48\( *\frac { 3 } {8 } \)]=18days

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