MAT Exam 2021 Paper

Concept:Work done is proportional to number of machines, working days, hours per day, and efficiency.Explanation:Let the required working hours per day be $x$.First group: $2$ machines, $8$ days, $12$ hours/day, efficiency $90\%$, work $= 9000$ tonnes.Second group: $3$ machines, $6$ days, $x$ hours/day, efficiency $80\%$, work $= 12000$ tonnes.Equate the work rates of both groups:$$\frac{2 \times 8 \times 12 \times 90}{9000} = \frac{3 \times 6 \times x \times 80}{12000}$$Simplify both sides:$$\frac{17280}{9000} = \frac{1440x}{12000}$$$$1.92 = 0.12x$$$$x = \frac{1.92}{0.12} = 16$$Answer:Each machine should work $\boxed{16}$ hours per day.Correct option: B. 16 h per day.