A's 2 days work is equal to B's 3 days work. If A can complete the work in 8 days, then to complete the work B will take ?

Answer: Option B

$$\begin{array}{rl}& \text{According to the question,}\\ & \Rightarrow 2\text{A}=\text{3B}\\ & \Rightarrow \frac{\text{A}}{\text{B}}=\frac{3}{2}\\ & \Rightarrow \text{Then efficiency ratio }\\ & \text{A}:\text{B}=3:2\end{array}$$
⇒ We know that time is inversely proportional to efficiency
⇒ Then time taken by them in ratio
$$\begin{array}{rl}& \text{A}:\text{B}=\underset{8\text{days}}{\underset{4\times \downarrow }{2}}:\underset{12\text{days}}{\underset{\downarrow \times 4}{3}}\\ & \because \text{A can do the work in 8 days}\\ & \Rightarrow \text{i}\text{.e, 2 units}\to \text{8}\\ & \text{1 unit}\to \text{4}\\ & \Rightarrow \text{Time taken by B}\to \text{3 units}\\ & =3\times 4\\ & =12\text{ days}\end{array}$$