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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 $(A).$

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 $(A).$

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Let $1^{st}$ number is $x$ and $2^{nd}$ number is $y.$

$\Rightarrow$ $\text{($\frac{1}{4}$ * ($60$%)*x})$ $=$ $\textrm{($\frac{2}{5}$ * ($20$%)*y)}$

$\Rightarrow$ $\text{$(\frac{60}{400}$)* x}$ $=$ $\textrm{$(\frac{40}{500}$)* y}$

$\Rightarrow$ $\frac{x}{y}$ $=$ $\frac{8}{15}$

So the ratio of the first number to that of the second number is= $8:15$

Option $A$ is correct here.

$\Rightarrow$ $\text{($\frac{1}{4}$ * ($60$%)*x})$ $=$ $\textrm{($\frac{2}{5}$ * ($20$%)*y)}$

$\Rightarrow$ $\text{$(\frac{60}{400}$)* x}$ $=$ $\textrm{$(\frac{40}{500}$)* y}$

$\Rightarrow$ $\frac{x}{y}$ $=$ $\frac{8}{15}$

So the ratio of the first number to that of the second number is= $8:15$

Option $A$ is correct here.