A and B can complete a task in 25 days. B alone can complete $$33 \frac{1}{3}$$% of the same task in 15 days. In how many days can A alone complete $$\frac{4}{15}{th}$$ of the same task?

A and B together can complete the task in 25 days

B alone can complete $$33\ \frac{\ 1}{3}\%\ ,i.e\ \frac{1}{3\ }$$ of the work in 15 days

So, B can complete the whole task in 45 days

Total work = LCM of 25 & 45 , i.e 225

$$Efficiency\ =\ \frac{\left(total\ wotk\right)}{time\ taken}$$

Efficiency of A and B together = $$\frac{225}{25}=9$$

Efficiency of B = $$\frac{225}{45}=5$$

Efficiency of A = 9 - 5 = 4

Time taken by A to complete the $$\frac{4}{15}$$ Total work = $$\frac{\left(\left(\frac{4}{15}\right)\times\ Total\ work\ \right)}{Efficiency\ of\ A}=\frac{\left(\frac{4}{15}\right)\times\ 225}{4}=15$$

Hence Option B is correct.