Let the work done by man and woman per day be \\\\(x\\\\) and \\\\(y\\\\) respectively.When the work is completed in \\\\(4\\\\) daysSince \\\\(5\\\\) men and \\\\(2\\\\) women complete the work in \\\\(4\\\\) daystherefore work done by \\\\(5\\\\) men and \\\\(2\\\\) women in \\\\(1\\\\) day \\\\(=\\\\) \\\\(\\cfrac{1}{4}\\\\)\\\\(\ herefore \\; 5x + 2y = \\cfrac{1}{4} \\longrightarrow \\; {eq}^{n} 1\\\\)When the work is completed in \\\\(3\\\\) daysSince \\\\(6\\\\) men and \\\\(3\\\\) women complete the work in \\\\(3\\\\) daystherefore work done by \\\\(6\\\\) men and \\\\(3\\\\) women in \\\\(1\\\\) day \\\\(=\\\\) \\\\(\\cfrac{1}{3}\\\\)\\\\(\ herefore \\; 6x + 3y = \\cfrac{1}{3} \\longrightarrow \\; {eq}^{n} 2\\\\)Multiplying by \\\\(3\\\\) in \\\\({eq}^{n} 1\\\\), we get\\\\(\\Rightarrow 15x + 6y = \\cfrac{3}{4} \\; \\longrightarrow \\; {eq}^{n} 3\\\\)Multiplying by \\\\(2\\\\) in \\\\({eq}^{n} 2\\\\), we get\\\\(\\Rightarrow 12x + 6y = \\cfrac{2}{3} \\; \\longrightarrow \\; {eq}^{n} 4\\\\)On subtracting \\\\({eq}^{n}\\\\) 4 from \\\\({eq}^{n}\\\\) 3, we get\\\\(\\Rightarrow 15x + 6y - 12x - 6y = \\cfrac{3}{4} - \\cfrac{2}{3}\\\\)\\\\(\\Rightarrow \\; 3x = \\cfrac{1}{12}\\\\)\\\\(\\Rightarrow \\; x = \\cfrac{1}{36}\\\\)On substituting the value of \\\\(x\\\\) in \\\\({eq}^{n} 2\\\\), we get\\\\(\\Rightarrow 6 \ imes \\cfrac{1}{36} + 3y = \\cfrac{1}{3}\\\\)\\\\(\\Rightarrow \\; 3y = \\cfrac{1}{3} - \\cfrac{1}{6}\\\\)\\\\(\\Rightarrow \\; y = \\cfrac{1}{18}\\\\)Thus,work done by \\\\(1\\\\) man in \\\\(1\\\\) day \\\\(=\\cfrac{1}{36}\\\\) days\\\\(\ herefore\\\\) Time taken by \\\\(1\\\\) man alone to finish the work \\\\(= 36\\\\) dayswork done by \\\\(1\\\\) woman in \\\\(1\\\\) day \\\\(= \\cfrac{1}{18}\\\\) days\\\\(\ herefore\\\\) Time taken by \\\\(1\\\\) woman alone to finish the work \\\\(= 18\\\\) days