Let the first number is $x$ and the second number is $y.$
Now, $\dfrac{1}{4} \times \dfrac{60}{100} \times x = \dfrac{2}{5} \times \dfrac{20}{100} \times y$
$\implies 15x = 8y$
$\implies \dfrac{x}{y} = \dfrac{8}{15}$
Hence, the respective ratio of the first number to that of second number $ = 8:15.$
So, the correct answer is $(A).$