9 men can complete a piece of work in 8 days, while 4 women can do it in 9 days. In how many days can 2 women and 4 men complete this work?

Correct option is C

​$$\textbf{Given:} \\9 \text{ men can complete the work in } 8 \text{ days} \\4 \text{ women can complete the work in } 9 \text{ days} \\\text{Required: Time taken by } 4 \text{ men and } 2 \text{ women} \\\\\textbf{Formula Used:} \\\text{Total Work} = \text{Number of persons} \times \text{Days} \\\text{Time} = \dfrac{\text{Total Work}}{\text{Daily Work}} \\\\\textbf{Solution:} \\\text{Total work in terms of men} = 9 \times 8 = 72 \text{ man-days} \\\\\text{Total work in terms of women} = 4 \times 9 = 36 \text{ woman-days} \\\text{Since total work is same:} \\72 \text{ man-days} = 36 \text{ woman-days} \\1 \text{ woman} = 2 \text{ men} \\2 \text{ women} = 2 \times 2 = 4 \text{ men} \\\\\text{Total effective men} = 4 \text{ men} + 4 \text{ men} = 8 \text{ men} \\\text{Daily work of 8 men} = 8 \text{ man-days per day} \\\\\text{Total work} = 72 \text{ man-days} \\\\\text{Required time} = \dfrac{72}{8} = 9 \text{ days} \\\\\textbf{Therefore, the work will be completed in } \boxed{9 \text{ days}}$$​​