• question_answer The work done by a woman in 8 h is equal to the work done by a man in 6 h and by a boy in 12 h. If working 6 h per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same work, working 8 h per day? A)  $2\frac{1}{2}$ days     B)         $1\frac{1}{2}$ days     C)         $3\frac{1}{2}$ days     D)         None of these

Given, 8 Women = 6 Men = 12 Boys $\therefore$12 Men + 12 Women + 12 Boys = 12 Men + 9 Men + 6 Men = 27 Men We have,           ${{M}_{1}}=9,\,\,{{D}_{1}}=6,\,\,{{t}_{1}}=6,\,\,{{w}_{1}}=1$ ${{M}_{2}}=27,\,\,{{D}_{2}}=?,\,\,{{t}_{2}}=8,\,\,{{w}_{2}}=1$ $\therefore$      ${{M}_{1}}{{D}_{1}}{{t}_{1}}{{w}_{2}}={{M}_{2}}{{D}_{2}}{{t}_{2}}{{w}_{1}}$ $\Rightarrow$   $9\times 6\times 6\times 1=27\times {{D}_{2}}\times 8\times 1$ $\Rightarrow$   ${{D}_{2}}=\frac{3}{2}$ days or $1\frac{1}{2}$ days