Sixteen men can finish a work in 8 days. Eight men and nine women working together can finish the same work in 10 days. In how many days will twenty women finish the same work?

12

Given,

16M x 8 = (8M + 9W) x 10 

⇒ 64M = 40M + 45W

⇒ 24M = 45W

⇒ M : W = 45 : 24 = 15 : 8   (Efficiency)

⇒ Total work = 16 (15) x 8 = 1920 units.   ..(Efficiency × Days = Total work)

⇒ Time required by 20 women to complete the work = \(\frac{1920}{20(8)}\) = \(\frac{1920}{160}\) = 12 days.   ..(\(\frac{Work}{Efficiency}\) = Time)