The price of rice increases by 25%, and as a result a man can purchase 5 kg less rice for Rs. 500 than before. What was the original price of rice per kilogram before the increase?

Introduction / Context:
This is a standard percentage and unitary method problem that appears frequently in aptitude exams. A fixed amount of money now buys less quantity after a price increase. By relating the change in quantity to the percent change in price, you can work backwards to find the original price per kilogram of rice.

Given Data / Assumptions:

Total money available to buy rice = Rs. 500.

Original price of rice per kilogram is unknown and is to be found.

Price of rice increases by 25%.

After the increase, the man can buy 5 kg less rice for the same Rs. 500.

Concept / Approach:
Let the original price of rice be P rupees per kilogram. Then the original quantity purchased is 500 / P kilograms. After a 25% increase, the new price becomes 1.25 * P rupees per kilogram, and the new quantity is 500 / (1.25 * P) kilograms. The difference in quantity is given to be 5 kg. Using this, we can form an equation and solve for P. This combines basic algebra with percentage increase ideas.

Step-by-Step Solution:
Step 1: Let the original price per kilogram be P rupees.Step 2: Original quantity the man could buy = 500 / P kilograms.Step 3: New price after 25% increase = 1.25 * P rupees per kilogram.Step 4: New quantity he can buy = 500 / (1.25 * P) kilograms.Step 5: According to the question, original quantity − new quantity = 5.So, 500 / P − 500 / (1.25 * P) = 5.Step 6: Simplify 500 / (1.25 * P) = 500 / (5P / 4) = 500 * 4 / (5P) = 400 / P.Step 7: Therefore, 500 / P − 400 / P = (500 − 400) / P = 100 / P = 5.Step 8: So 100 / P = 5 implies P = 100 / 5 = Rs. 20.

Verification / Alternative check:
If the original price is Rs. 20 per kilogram, original quantity = 500 / 20 = 25 kg. New price after 25% increase = 20 * 1.25 = Rs. 25 per kilogram. New quantity = 500 / 25 = 20 kg. The reduction in quantity is 25 − 20 = 5 kg, which matches the problem statement. So the solution is correct.

Why Other Options Are Wrong:
Rs. 24, Rs. 26, and Rs. 29 do not satisfy the given condition when you compute original and new quantities with a 25% increase. The difference in quantities will not be exactly 5 kg in those cases.
Rs. 18 also fails to give a reduction of 5 kg when the same method is applied.

Common Pitfalls:
Candidates often try to work with percentage change directly on quantity instead of forming a clear equation. Forgetting that price and quantity are inversely related for a fixed budget also leads to mistakes. Another frequent error is miscalculating the new price after percentage increase. Always express the new price as (1 + percentage increase) times the original price and then use the difference in quantities to derive the correct equation.

Final Answer:
The original price of rice was Rs. 20 per kilogram.