As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹1,200. What was the original price of rice per kg?

Correct Answer: ₹40

Let us solve this problem step-by-step to find the original price of rice per kg.

Step 1: Understand the given information
Total amount spent = ₹1,200
Percentage increase in price = 25%
Decrease in quantity of rice purchased = 6 kg

Step 2: Define variables
Let the original price of rice per kg be $x$ rupees.

Step 3: Express original and new prices
Original price per kg = $x$
Increased (New) price per kg = $x+0.25x=1.25x$ or $\frac{5}{4}x$

Step 4: Express the quantity of rice purchased
Original quantity purchased = $\frac{1200}{x}$ kg
New quantity purchased = $\frac{1200}{1.25x}$ kg

Step 5: Set up the equation
According to the question, the difference between the original quantity and the new quantity is 6 kg.

$\frac{1200}{x}-\frac{1200}{1.25x}=6$

Step 6: Solve for $x$
Simplify $\frac{1200}{1.25}$:

$\frac{1200}{1.25}=960$

Substitute this back into the equation:

$\frac{1200}{x}-\frac{960}{x}=6$

$\frac{1200-960}{x}=6$

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

$6x=240$

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

$x=40$

Conclusion:
The original price of rice per kg was ₹40.