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 ?

Solution(By Examveda Team)

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