To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

$$\eqalign{ & {\text{We have}} \cr & {\text{B}} = \frac{3}{2} \times {\text{A}} \cr & \to {\text{A}} = \frac{2}{3} \times {\text{B}} \cr & {\text{One day's work,}} \cr & \Rightarrow {\text{A}} + {\text{B}} = \frac{1}{{18}} \cr & \Rightarrow \frac{2}{3} \times {\text{B}} + {\text{B}} = \frac{1}{{18}} \cr & \Rightarrow \frac{5}{3} \times {\text{B}} = \frac{1}{{18}} \cr & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}}\,{\text{B}} \cr & = \frac{3}{{90}} \cr} $$
B alone can complete the work in
$$\eqalign{ & = \frac{{90}}{3} \cr & = 30\,{\text{days}} \cr} $$