MAT Exam 2023 Paper

Concept:Work done is constant. Use efficiency ratio and the work equivalence formula $M_1D_1 = M_2D_2$.Explanation:A woman takes twice the time taken by a boy, so a boy is twice as efficient as a woman.Let efficiency of a woman = $1$ unit/day and efficiency of a boy = $2$ units/day.Total work done by 8 women and 12 boys in 9 days:$$(8 \times 1 + 12 \times 2) \times 9 = (8 + 24) \times 9 = 288 \text{ units}$$Let 12 boys finish the same work in $D$ days.Work done by 12 boys in $D$ days:$$12 \times 2 \times D = 24D$$Equating total work:$$24D = 288 \Rightarrow D = 12$$Thus, 12 boys will finish the work in 12 days.Answer:$12$ days, which is Option D.