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?

Total work = man/woman $$\times$$ time

Work is same so,

16m $$\times 8 = (8m + 9w) \times 10

$$\Rightarrow$$ 128m = 80m + 90w

$$\Rightarrow$$ 48m = 90w

$$\Rightarrow$$ 8m = 15w 

Let the 20 women complete work in days so,

Total work = 20w $$\times$$ d

$$\Rightarrow$$ (8m + 9w) \times 10 = 20w $$\times$$ d

$$\Rightarrow$$ (15w + 9w) \times 10 = 20w $$\times$$ d

$$\Rightarrow$$ 24w \times 10 = 20w $$\times$$ d

$$\Rightarrow$$ d = 12 days

$$\therefore$$ Twenty women finish the same work in 12 days.