A woman goes to the market with Rs. 500 to buy oranges; due to a 10% decrease in the price of oranges, she is able to buy 2 kg more for the same amount; what was the original price per kilogram of oranges?

Introduction / Context:
This question is a classic application of percentage change in price and corresponding change in quantity for a fixed budget. The woman has a fixed amount of money and, when the price of oranges drops by a certain percentage, she can buy more kilograms than before. We need to work backward from the change in quantity and the price reduction to find the original price per kilogram.

Given Data / Assumptions:

• Total money available with the woman = Rs. 500.
• Price of oranges decreases by 10%.
• Because of this price decrease, she can buy 2 kg more oranges with the same Rs. 500.
• We assume that all money is spent on oranges before and after the price change.
• We need to determine the original price per kilogram.

Concept / Approach:
Let the original price per kilogram of oranges be P. Then the original quantity she can buy is 500 / P. After a 10% price decrease, the new price per kilogram becomes 0.9P. At this new price, the quantity she can buy is 500 / (0.9P). According to the question, this new quantity is exactly 2 kg more than the original quantity. This gives a simple equation involving P. Solving that equation yields the original price per kilogram.

Step-by-Step Solution:
Step 1: Let the original price per kg of oranges be P rupees.Step 2: Original quantity of oranges she can buy = 500 / P kg.Step 3: New price per kg after 10% decrease = 0.9 * P.Step 4: New quantity she can buy at reduced price = 500 / (0.9P) kg.Step 5: According to the problem, the new quantity is 2 kg more than the original quantity.Step 6: So we write the equation: 500 / (0.9P) = 500 / P + 2.Step 7: Simplify left side: 500 / (0.9P) = (500 / P) * (1 / 0.9).Step 8: Let Q = 500 / P; then we have Q * (1 / 0.9) = Q + 2.Step 9: So Q / 0.9 = Q + 2.Step 10: Multiply both sides by 0.9: Q = 0.9Q + 1.8.Step 11: Rearranging: Q - 0.9Q = 1.8, so 0.1Q = 1.8 and Q = 18.Step 12: Recall that Q = 500 / P, so 500 / P = 18.Step 13: Therefore P = 500 / 18 ≈ 27.777..., that is about Rs. 27.78 per kg.

Verification / Alternative check:
Use P ≈ 27.78. Original quantity = 500 / 27.78 ≈ 18 kg. New price after 10% decrease is 27.78 * 0.9 ≈ 25.00. With new price 25, quantity = 500 / 25 = 20 kg. This is exactly 2 kg more than 18 kg, as required. The options are rounded to two decimal places, so Rs. 27.77 closely matches the calculation and is the best choice.

Why Other Options Are Wrong:

• Rs. 22.77 and Rs. 25.77: These give different original quantities and do not lead to exactly 2 kg difference after a 10% price cut.
• Rs. 29.77: This would give a smaller original quantity and would not produce the specified 2 kg increase with a 10% decrease in price.

Common Pitfalls:

• Applying the 10% reduction incorrectly, such as subtracting 10 in rupees instead of 10% of the price.
• Setting up the equation with the difference in price rather than the difference in quantities.
• Rounding too early in calculations, which can slightly distort the final answer if not handled carefully.

Final Answer:
The original price of the oranges was approximately Rs. 27.77 per kilogram.