As a result of $25\%$ hike in the price of rice per kg, a person is unable to purchase $6\text{kg}$ more rice for $₹1,200$. What was the original price of rice per kg?

Note: Based on the logical construction of price-hike and consumption problems, a price increase causes a person to buy less quantity, not more. The Hindi text correctly implies "कम चावल खरीद पाता है" (buys less rice). We will solve it accordingly.
Let the original price of rice per kg be $₹x$.
Total money spent = $₹1,200$.

$$\text{Original quantity purchased}=\frac{1,200}{x}\text{kg}$$

New price after a $25\%$ hike:

$$\text{New Price}=x+25\%\text{ of }x=1.25x=\frac{5}{4}x$$

$$\text{New quantity purchased}=\frac{1,200}{\frac{5}{4}x}=\frac{4,800}{5x}=\frac{960}{x}\text{kg}$$

According to the question, the difference in quantity is $6\text{kg}$:

$$\frac{1,200}{x}-\frac{960}{x}=6$$

$$\frac{240}{x}=6$$

$$6x=240$$

$$x=\frac{240}{6}=40$$

Thus, the original price of rice per kg was $₹40$.