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 = ?

Solution(By Examveda Team)

Let time taken by A alone in doing work be x days
∴ Time taken by B alone = 3x days
$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{x} \cr & {\text{B's 1 days work}} = \frac{1}{{3x}} \cr & \because {\text{A and B together finish}} \cr & = \frac{2}{5}{\text{work in 9 days}}{\text{.}} \cr} $$
∴ Time taken by A and B in doing whole work
$$\eqalign{ & = \frac{{9 \times 5}}{2} \cr & = \frac{{45}}{2}{\text{ days}} \cr} $$
According to given information we get
$$\eqalign{ & \therefore \frac{1}{x} + \frac{1}{{3x}} = \frac{2}{{45}} \cr & \Rightarrow \frac{{3 + 1}}{{3x}} = \frac{2}{{45}} \cr & \Rightarrow \frac{4}{{3x}} = \frac{2}{{45}} \cr & {\text{By cross - multiply we get }} \cr & \Rightarrow 2 \times 3x = 4 \times 45 \cr & \Rightarrow x = \frac{{4 \times 45}}{{2 \times 3}} \cr & \Rightarrow x = 30{\text{ days}} \cr & {\text{Time taken by A}} \cr & = x{\text{ days}} \cr & = {\text{30 days}} \cr & \therefore {\text{Time taken by B}} \cr & = 3x{\text{ days}} \cr & = 3 \times 30 \cr & = 90{\text{ days}} \cr} $$