Due to a price hike of 20 percent, 4 kg less sugar can be bought for Rs. 120 than before. What was the initial price per kilogram of sugar before the increase?

Introduction / Context:
This problem combines unitary method with percentage increase. The same amount of money, Rs. 120, now buys 4 kg less sugar because the price has gone up by 20 percent. You must work backward to find the original price per kilogram. Such questions are very common in topics involving inflation, cost of living, and price rise calculations.

Given Data / Assumptions:

• Money available = Rs. 120.
• Initial price of sugar = x rupees per kg.
• New price after 20 percent increase = 1.2x rupees per kg.
• 4 kg less sugar can be bought for the same Rs. 120 after the price hike.

Concept / Approach:
We express the quantity of sugar that can be bought before and after the price rise in terms of x. Before the rise, quantity = 120 / x kg. After the rise, quantity = 120 / (1.2x) kg. The difference between the two quantities is given as 4 kg. Setting up this equation and solving for x gives the initial price per kilogram.

Step-by-Step Solution:
Step 1: Quantity before hike = 120 / x kg.Step 2: New price = 1.2x, so quantity after hike = 120 / (1.2x) = 100 / x kg.Step 3: Given that the new quantity is 4 kg less, so (120 / x) − (100 / x) = 4.Step 4: Simplify the left side: (120 − 100) / x = 20 / x.Step 5: Therefore 20 / x = 4, giving x = 20 / 4 = 5.Step 6: Initial price per kg of sugar = Rs. 5 per kg.

Verification / Alternative check:
At Rs. 5 per kg, before the increase, quantity = 120 / 5 = 24 kg. New price after 20 percent rise = 1.2 * 5 = Rs. 6 per kg, so new quantity = 120 / 6 = 20 kg. The difference = 24 − 20 = 4 kg, which matches the problem statement. This confirms that the original price is correct.

Why Other Options Are Wrong:
Option 4 per kg would yield 30 kg before and 25 kg after a 20 percent increase to Rs. 4.8 per kg, a difference of 5 kg, not 4 kg. Option 6 per kg and option 5.5 per kg do not satisfy the difference condition when checked similarly. Option 3 per kg would produce an even larger error in the quantity difference.

Common Pitfalls:

• Using 20 rupees rather than 20 percent as the increase in price.
• Forgetting to apply the new price of 1.2x correctly to find the new quantity.
• Incorrect algebra when forming or simplifying the equation involving x.

Final Answer:
The initial price of sugar was Rs. 5 per kg.