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Discussion :: Time and Work

  1. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?

  2. A.

    11:30 A.M.

    B.

    12 noon

    C.

    12:30 P.M.

    D.

    1:00 P.M.

    View Answer

    Workspace

    Answer : Option D

    Explanation :

    (P + Q + R)'s 1 hour's work =[\(\frac { 1 } {8 } \)+\(\frac { 1 } {10 } \)+\(\frac { 1 } {12 } ]\)=\(\frac { 37 } {120} \)

     

    Work done by P, Q and R in 2 hours =[\(\frac { 37 } {120} \)*2]=\(\frac { 37 } {60} \)

     

    Remaining work =\([1-\frac { 37 } {60 } ]\)=\(\frac { 23 } {60} \)

     

    (Q + R)'s 1 hour's work =[\( \frac { 1 } { 10 }\)+\( \frac { 1 } { 12 }\)]=\(\frac {11 } {60} \)

     

    Now,   \(\frac {11 } {60} \) work is done by Q and R in 1 hour

     

    So,\(\frac { 23 } {60} \)work will be done by Q and R in[\(\frac { 60 } { 11 }\)\( *\frac { 23 } {60 } \)]=\(\frac { 23 } {11} \)hours = 2 hours.

     

    So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.


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