A can do in one day 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 is = ?

Answer: Option A

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