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

Let the original price of rice be $₹x$ per kg.
Total amount spent = $₹8,000$

Original quantity purchased = $\frac{8000}{x}\text{ kg}$

The price is reduced by $20\%$.

$$\text{New Price}=x-0.20x=0.80x=\frac{4}{5}x$$

New quantity purchased = $\frac{8000}{0.80x}=\frac{10000}{x}\text{ kg}$

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

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

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

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

$$x=16$$

Thus, the original price of rice per kg is $₹16$.