MAT Exam 2022 Paper

Concept:If men and days change but the nature of work remains the same, then $\frac{\text{men} \times \text{days}}{\text{work}}$ remains constant.Explanation:Let the required number of days be $D$.Use the relation: $\frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2}$.Here, $M_1 = 30$, $D_1 = 25$, $W_1 = 15$.Also, $M_2 = 14$, $W_2 = 7$, and $D_2 = D$.Substitute these values:$\frac{30 \times 25}{15} = \frac{14 \times D}{7}$Simplify the left side: $\frac{750}{15} = 50$.Simplify the right side: $\frac{14D}{7} = 2D$.So, $50 = 2D$.Therefore, $D = \frac{50}{2} = 25$ days.Answer:14 men will complete 7 projects in 25 days.Correct option: B. 25 days.