A can finish one-third of a work in 5 days, B can finish $$\frac{2}{5}th$$ of the same workin 10 days and C can finish 75% of the same work in 15 days. They work together for 6 days. The remaining work will be finished by B alone in:

A can finish complete  work = $$3\times 5 $$ = 15 days

B can finish complete work = $$ \dfrac{5}{2}\times 10 $$ = 25 days

C can finish complete work = $$ \dfrac{9}{3}\times 15 $$ = 20 days 

work completed by A +B + C in 6 days

$$\Rightarrow (\dfrac {1}{15} + \dfrac{1}{25}+ \dfrac{1}{20}) \times 6 $$

$$\Rightarrow (\dfrac{20+12+15}{300})\times 6 $$

$$\Rightarrow \dfrac{47}{50}$$

then Remaining work = $$  1 - \dfrac{47}{50} $$

$$\Rightarrow \dfrac{3}{50}$$ 

Remaining work will finish  B = $$\dfrac {3}{50} \times 25 days $$

$$\Rightarrow \dfrac{3}{2}$$ days

$$\Rightarrow 1 \dfrac{1}{2}$$days Ans