5 men and 8 women can complete a work in 12 days working together, while man and 7 women together can complete the same work in 15 days. In how many days will 11 women complete the same work?

\(\frac{108}{11}\)

5M + 8W = 12 days, 

60M + 96W        ..(1)       (Multiplied by 12 to get it done in 1 day)

M + 7W = 15 days,

15M + 105W     ..(2)        (Multiplied by 15 to get it done in 1 day)

Now, (1) - (2), we get

⇒ 45M = 9W

⇒ M : W = 9 : 45 = 1 : 5 (Efficiencies)

Putting efficiency in equation (2), and we get the total work 

⇒ [15 (1) + 105 (5)] = 525 units.

Now, total efficiency of 11W = 11(5) = 55

⇒ Required time = (\(\frac{Work}{Efficiency}\) = Time ) = \(\frac{525}{55}\) = \(\frac{108}{11}\) days.