One-fourth of sixty percent of a number is equal to two-fifth of twenty percent of another number. What is the respective ratio of the first number to the second number ?

Let the first number be x and the second number be y
$$\frac{1}{4}{\text{ of 60% of }}x = \frac{2}{5}{\text{ of 20% of }}y$$
$$\eqalign{ & \Rightarrow \frac{1}{4} \times \frac{{60}}{{100}} \times x = \frac{2}{5} \times \frac{{20}}{{100}} \times y \cr & \Rightarrow \frac{{3x}}{{20}} = \frac{{2y}}{{25}} \cr & \Rightarrow \frac{x}{y} = \frac{2}{{25}} \times \frac{{20}}{3} \cr & \Rightarrow \frac{x}{y} = \frac{8}{{15}} \cr} $$