3 men and 4 women can do a work in 12 days. 5 men and 3 women can do that work in 10 days. Only 11 women can finish the same work in

\(\frac{60}{7}\) days

According to the question,

(3M + 4W) x 12 = (5M + 3W) x 10

(Men x days = Work)

36M + 48W = 50M + 30W

        18W    =    14M

            M    =   \(\frac{9}{7}\)W                 

Total Work = (3M + 4W) x 12 = (3 x \(\frac{9}{7}\)W  + 4W) x 12 = \(\frac{55\; \times\; 12}{7}\)W 

Time taken by 11 women to complete the work = \(\frac{Work}{Women}\) = \(\frac{(55\; \times\; 12)W}{7\; \times\; 11W}\) 

                                                                     = \(\frac{60}{7}\) days