According to the question,

In 1 day,

(1 man+ 1 women +1 child)'s can complete $\frac{1}{3}$^th of the work

∴ 1 Woman can complete $=\frac{1}{3}-\frac{1}{6}-\frac{1}{18}\Rightarrow \frac{6-3-1}{18}=\frac{1}{9}$^th of the work

So, the woman alone can complete the work in 9 days.

Hence option A is the correct.