12 men and 12 women  can complete a piece of work in 9 days. 6 men and 15 women can complete the same work in 12 days. How long (in days) would it take 9 women to complete half the work ? 

18 

12M + 12W = 9 days

108M + 108W          ..(1)    (Multiplied by 9 to get it in 1 day)

6M + 15W = 12 days

72M + 180W             ..(2)    (Multiplied by 12 to get it in 1 day)

⇒ NOW, (1) - (2), WE GET 

⇒ 36M = 72W

⇒ M : W = 72 : 36 = 2 : 1 (Efficiencies)

Putting efficiency in equation (1), and get the total work

⇒ 108(2) + 108(1) 

⇒ 324 units.

now the time it would take 9 women to complete half the work = \(\frac{324}{2}\) = 162 units 

⇒ \(\frac{162}{9(1)}\) = 18 days.