8 men and 3 women can do a piece of work in 7 days, whereas 5 men and 1 woman can do it in 12 days. How many men should assist 8 women so that the same work is completed in $$4\frac{1}{5}$$​ days?

Correct option is B

​$$\textbf{Given :} \\\ \, \\8m + 3w \text{ do work in } 7 \text{ days} \\\ \, \\5m + w \text{ do work in } 12 \text{ days} \\\ \, \\\text{Required time} = 4\frac{1}{5} = \frac{21}{5} \text{ days} \\\ \, \\\textbf{Formula Used :} \\\ \, \\\text{Work} = \text{Efficiency} \times \text{Time} \\\ \, \\\textbf{Solution :} \\\ \, \\7(8m + 3w) = 12(5m + w) \\\ \, \\56m + 21w = 60m + 12w \\\ \, \\9w = 4m \Rightarrow \frac{w}{m} = \frac{4}{9} \\\ \, \\\text{Let efficiency of 1 woman} = 4 \text{ units} \\\ \, \\\text{Let efficiency of 1 man} = 9 \text{ units} \\\ \, \\\text{Daily work} = 8(9) + 3(4) = 84 \text{ units} \\\ \, \\\text{Total work} = 84 \times 7 = 588 \text{ units} \\\ \, \\\text{Let required men} = x \\\ \, \\\text{Daily work} = 9x + 8(4) = 9x + 32 \\\ \, \\(9x + 32) \times \frac{21}{5} = 588 \\\ \, \\9x + 32 = 140 \\\ \, \\9x = 108 \Rightarrow x = 12 \\\ \, \\\textbf{Final Answer :} \\\ \, \\12 \, days$$​​