A and B can do a piece of work in 25 days. B alone can do $$66\frac{2}{3}\% $$  of the same work in 30 days. In how many days can A alone do $$\frac{4}{{15}}$$ part of the same work?

$$\eqalign{ & 66\frac{2}{3}\% \to 30{\text{ days}} \cr & \frac{2}{3} \to 30{\text{ days}} \cr & 1 \to 45{\text{ days}} \cr} $$

$$\eqalign{ & {\text{A}} = 4{\text{ unit}} \cr & {\text{A}} = \frac{{25 \times \frac{4}{{15}}}}{4} \cr & {\text{A}} = 15{\text{ days}} \cr} $$