A can do in one day three times the work done by B in one day. They together finish $$\ \frac{2}{5}\ $$of the work in 9 days. The number of days by which B can do the work alone is:

Let total work to be done = $$5y$$ units

Let B's efficiency = $$x$$ units/day

=> A's efficiency = $$3x$$ units/day

Work done by (A+B) together in 1 day = $$(x+3x)=4x$$ units/day

=> Work done in 9 days = $$9\times4x=36x$$ units --------------(i)

Also, according to ques, work done in 9 days = $$\frac{2}{5}\times5y=2y$$ units ------------(ii)

=> $$36x=2y$$

=> $$\frac{y}{x}=\frac{36}{2}=18$$ -----------(iii)

$$\therefore$$ Number of days by which B can do the work alone = $$\frac{5y}{x}$$

= $$5\times\frac{y}{x}=5\times18=90$$ days

=> Ans - (D)