According to the question,

In 1 day,

Ayesha can complete $\frac{1}{16}$^th of the work 

Amita can complete $\frac{1}{8}$^th of the work

Ayesha and Amita together can complete 

$=\frac{1}{16}+\frac{1}{8}=\frac{1+2}{16}=\frac{3}{16}$ ^th of the work

∴ Ayesha and Amita together can complete the work  in $\frac{16}{3}$or $5\frac{1}{3} days$

Hence option C is the correct.