MAT Exam 2020 Paper

Concept:Convert all workers into equivalent men using the given relation of work capacities, then compare total men-hours required for the two pieces of work.Explanation:Given that 15 men, 24 women, and 36 boys do the same work in the same time, their capacities are equivalent:$15$ men $= 24$ women $= 36$ boys.First, express 12 women and 6 boys in terms of men.$1$ woman $= \frac{15}{24} = \frac{5}{8}$ men.So, $12$ women $= 12 \times \frac{5}{8} = \frac{15}{2}$ men.$1$ boy $= \frac{15}{36} = \frac{5}{12}$ men.So, $6$ boys $= 6 \times \frac{5}{12} = \frac{5}{2}$ men.Total already working $= \frac{15}{2} + \frac{5}{2} = 10$ men.Now, the original work is done by 15 men in 12 days, working 8 hours per day.Total man-hours for original work $= 15 \times 12 \times 8$.The new work is $2\frac14 = \frac94$ times as large.Let the total number of men required for the new work be $x$.Since the new work is done in 30 days working 6 hours per day:$$x \times 30 \times 6 = \frac94 \times 15 \times 12 \times 8$$$$x = \frac94 \times \frac{15 \times 12 \times 8}{30 \times 6} = \frac94 \times 8 = 18$$Total man-equivalent required $= 18$ men.Extra men needed $= 18 - 10 = 8$.Answer:8 men must be associated. Correct option: C.