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?

15

A + B = 25 days,

B = \(\frac{2}{3}\) W =30 = 45 days, 

⇒ So, Time required for A to complete \(\frac{4}{15}\) of total work = 225 x \(\frac{4}{15}\) = 60 units,

⇒ A + B = 9

⇒ Therefore, A = 4, (Efficiency)

⇒ \(\frac{60}{4}\) = 15 days