With a $5\%$ discount on the cost of sugar, a buyer could purchase $2\text{ kg}$ more sugar for $\text{Rs. }608$. What is the original selling price of sugar per kg?

Let the original price of sugar per kg be $\text{Rs. }x$.
The reduction in price is $5\%$, so the discounted price per kg becomes:

$$x-0.05x=0.95x$$

According to the given condition, the difference in quantity purchased for $\text{Rs. }608$ is $2\text{ kg}$:

$$\frac{608}{0.95x}-\frac{608}{x}=2$$

Taking $\frac{608}{x}$ common:

$$\frac{608}{x}\left(\frac{1}{0.95}-1\right)=2$$

$$\frac{608}{x}\left(\frac{100}{95}-1\right)=2$$

$$\frac{608}{x}\left(\frac{5}{95}\right)=2$$

$$\frac{608}{x}\left(\frac{1}{19}\right)=2$$

$$\frac{32}{x}=2$$

$$2x=32⟹x=16$$

Thus, the original selling price of sugar is $\text{Rs. }16\text{ per kg}$.