If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

$$\eqalign{ & {\text{Let}}\,40\% \,{\text{of}}\,A = \frac{2}{3}B \cr & {\text{Then}},\,\frac{{40A}}{{100}} = \frac{{2B}}{3} \cr & \Rightarrow \frac{{2A}}{5} = \frac{{2B}}{3} \cr & \Rightarrow \frac{A}{B} = {\frac{2}{3} \times \frac{5}{2}} = \frac{5}{3} \cr & \therefore A:B = 5:3 \cr} $$