MAT Exam 2022 Paper

Concept:Work done is measured in total person-hours, and since all three have equal ability, their hourly work rates are the same.Explanation:Third person alone works for 29 days at 16 hours per day.So total work $= 16 \times 29 = 464$ person-hours.Total work done by all three individually is also the sum of their total working hours.Thus, $m \times m + n \times n + 16 \times 16 = 464$.This gives $m^2 + n^2 + 256 = 464$, so $m^2 + n^2 = 208$.The integer pair satisfying this is $(12, 8)$, since $12^2 + 8^2 = 144 + 64 = 208$.Working together, their combined rate per day is $m + n + 16 = 12 + 8 + 16 = 36$ person-hours per day.Time required $= \frac{464}{36} \approx 12.89$ days.So they can complete the work in about 13 days.Answer:Option B: 13 days.