A can do 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 are ?

Solution(By Examveda Team)

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
$$\eqalign{ & {\text{Total work}} \cr & = {\text{days}} \times {\text{efficiency }}\left( {{\text{A}} + {\text{B}}} \right) \cr & = \frac{{45}}{2} \times 4 \cr & = 90 \cr & {\text{Number of days for B }} \cr & {\text{ = }}\frac{{{\text{Total work}}}}{{{\text{Efficiency}}}} \cr & = \frac{{90}}{1} \cr & = 90{\text{ days}} \cr} $$