According to the question,

16 men and 12 women together can complete a work in 8 days and 20 men can complete the same work in 16 days

So, (16 men+12 women)×8 days=20 men×16 days

⇒ 16 men+12 women=40 men

⇒ 12 women=(40-16)=24 men

∴ 1 woman = 2 men    ...(1)

⇒ 16 women =32 men ...(2)

Now, 20 men can complete the work 16 day's

So, 32 men can complete the same work in $\left(\frac{16\times 20}{32}\right)days=10 days$

as 1 woman = 2 men

16 women can complete the same work in 10 days

Hence option E is the correct.