When the price of rice decreases by 10%, a girl can buy 1 kg more rice for Rs. 270. What was the original price of rice per kilogram?

Introduction / Context:
This question is a typical application of percentage decrease in price leading to an increase in quantity purchasable with the same amount of money. It combines unitary method, percentages, and simple algebra. Such problems are frequently asked in exams under the topics of percentage, profit and loss, and consumption changes because they illustrate the inverse relationship between price and quantity for a fixed budget.

Given Data / Assumptions:

• A girl spends Rs. 270 on rice.
• When the price of rice decreases by 10%, she can buy 1 kg more rice for the same Rs. 270.
• We are asked to find the original price of rice per kilogram.
• The price change is a 10% decrease from the original price.
• No other changes in spending or consumption are mentioned.

Concept / Approach:
Let the original price of rice be P rupees per kilogram. After a 10% decrease, the new price becomes 0.9P. With Rs. 270, the quantity of rice that can be bought at the original price is 270 / P kilograms, and the quantity at the reduced price is 270 / (0.9P) kilograms. The problem states that this new quantity is exactly 1 kg more than the old quantity. We translate that condition into an equation and solve for P. This algebraic approach neatly links the price decrease percentage with the change in quantity.

Step-by-Step Solution:
Step 1: Let the original price be P rupees per kg.Step 2: After a 10% decrease, the new price is 90% of P, that is 0.9P rupees per kg.Step 3: Quantity bought at original price = 270 / P kg.Step 4: Quantity bought at reduced price = 270 / (0.9P) kg.Step 5: According to the question, the new quantity is 1 kg more than the old quantity: 270 / (0.9P) = 270 / P + 1.Step 6: Simplify 270 / (0.9P). Note that 270 / (0.9P) = 270 / P * (1 / 0.9) = (270 / P) * (10/9) = 300 / P.Step 7: So the equation becomes 300 / P = 270 / P + 1.Step 8: Subtract 270 / P from both sides: (300 / P) - (270 / P) = 1, which simplifies to 30 / P = 1.Step 9: Therefore P = 30.Step 10: The original price of rice is Rs. 30 per kg.

Verification / Alternative check:
At the original price of Rs. 30 per kg, Rs. 270 buys 270 / 30 = 9 kg of rice. After a 10% decrease, the new price is 90% of 30 = Rs. 27 per kg. At this price, Rs. 270 buys 270 / 27 = 10 kg of rice. The difference in quantity is 10 - 9 = 1 kg, which matches the condition given in the problem. Thus, the solution P = 30 is fully verified and consistent.

Why Other Options Are Wrong:
If the original price were Rs. 36, after a 10% decrease it would be Rs. 32.40. Then Rs. 270 would buy approximately 7.5 kg and 8.33 kg, not differing by exactly 1 kg. If the price were Rs. 28, the new price would be Rs. 25.20, and the resulting quantities would not differ by precisely 1 kg. If the price were Rs. 40, the new price would be Rs. 36, and the quantities would again not satisfy the 1 kg difference. Rs. 32 similarly fails to produce the required change. Only Rs. 30 leads to exactly 1 kg additional rice for Rs. 270 after a 10% price decrease.

Common Pitfalls:
Some learners confuse the base for the 10% decrease, incorrectly subtracting 10 rupees instead of 10% of the price. Others mis-handle the algebraic equation and fail to simplify 270 / (0.9P) correctly, or they do not realise that the increase in quantity must be exactly 1 kg. Using trial and error with options can be time consuming and error-prone. Writing a clear equation from the relationship and simplifying step by step is the most reliable strategy.

Final Answer:
The original price of rice was Rs. 30 per kilogram.