A reduction of $20\%$ in the price of rice enables a customer to purchase $125\text{ kg}$ more for $\text{Rs. }8,000$. What is the original price of rice per kg?

Let the original price of rice be $\text{Rs. }x$ per kg.
Total amount = $\text{Rs. }8,000$.
Original quantity purchased = $\frac{8000}{x}\text{ kg}$.

Reduced price = $x-20\%\text{ of }x=0.8x$ per kg.
New quantity purchased = $\frac{8000}{0.8x}=\frac{10000}{x}\text{ kg}$.

According to the question, the difference in quantity is $125\text{ kg}$:

$$\frac{10000}{x}-\frac{8000}{x}=125$$

$$\frac{2000}{x}=125$$

$$x=\frac{2000}{125}=16$$

Thus, the original price of rice was $\text{Rs. }16$ per kg.