A can do three times the work done by B in one day. They together finish 2/5 of the work in 9 days. The number of days by which B can do the work alone are ?

Answer: Option D

Efficiency of A = 3 efficiency of B
$$\left(\text{A}=3,\text{B}=1\right)$$
$$\frac{2}{5}$$ th of the work done by (A + B) in 9 days
Total work (A + B) = $$\frac{45}{2}$$ days will be completed
$$\begin{array}{rl}& \text{Total work}\\ & =\text{days}\times \text{efficiency }\left(\text{A}+\text{B}\right)\\ & =\frac{45}{2}\times 4\\ & =90\\ & \text{Number of days for B }\\ & \text{ = }\frac{\text{Total work}}{\text{Efficiency}}\\ & =\frac{90}{1}\\ & =90\text{ days}\end{array}$$