Due to a price hike of 20%, 4 kg less sugar is available for Rs 120 than before. What was the initial price per kg of sugar before the increase?

Introduction / Context:
This is a percentage and unit cost question involving a fixed amount of money and a change in price. When price increases, the same amount of money buys less quantity. The decrease in quantity, along with the percentage change, allows us to find the original price per kilogram.

Given Data / Assumptions:
- Original price of sugar = Rs p per kg. - Price increases by 20%, so new price = 1.2p per kg. - Budget for sugar = Rs 120. - Due to the increase, 4 kg less sugar is obtained for Rs 120 than before.

Concept / Approach:
Initially, quantity bought for Rs 120 is 120 / p kg. After the price hike, quantity is 120 / (1.2p) kg. The difference between these two quantities is given as 4 kg. This leads to an equation in p, which we can solve to find the original price per kilogram.

Step-by-Step Solution:
Step 1: Original quantity for Rs 120 = 120 / p kg. Step 2: New price after 20% increase = 1.2p. Step 3: New quantity for Rs 120 = 120 / (1.2p) kg. Step 4: Simplify 120 / (1.2p) = 100 / p. Step 5: According to question, original quantity minus new quantity = 4. Step 6: So, 120 / p - 100 / p = 4. Step 7: This gives 20 / p = 4, so p = 20 / 4 = 5.

Verification / Alternative check:
At original price Rs 5 per kg, Rs 120 buys 120 / 5 = 24 kg. After 20% increase, new price = 1.2 * 5 = Rs 6 per kg. Now Rs 120 buys 120 / 6 = 20 kg. The reduction is 24 - 20 = 4 kg, which matches the question exactly. So the answer is consistent.

Why Other Options Are Wrong:
- Rs 4, Rs 4.5, Rs 5.5 and Rs 6 per kg do not produce a difference of exactly 4 kg when recalculated. - In each wrong case, either the percentage increase or the quantity difference fails to match the given data.

Common Pitfalls:
A common mistake is to apply the percentage increase directly to the quantity instead of the price. Others forget to convert 20% to a factor of 1.2 or mishandle the fraction simplification from 120 / (1.2p) to 100 / p. Keeping track of units and operations on price versus quantity is essential.

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