A shopkeeper X sells fruits at a profit of 21%. If X had bought the fruits for 9% less and sold them for Rs 29 less, he would have earned a profit of 25%. What is the original cost price of the fruits?

Introduction / Context:
This is a layered percentage problem involving two hypothetical scenarios. X sells fruits at 21% profit in the original case. In an imaginary second case, both cost price and selling price are changed, and the profit becomes 25%. By comparing the two situations, we can determine the original cost price. This type of question tests your ability to form and solve equations with percentage changes applied to both cost and selling prices.

Given Data / Assumptions:

• Original profit = 21%.
• If fruits had been bought 9% cheaper, the new cost price would be 91% of original cost price.
• In the hypothetical case, fruits are sold for Rs 29 less than original selling price.
• Under that scenario, profit would be 25%.
• We need to find the original cost price.

Concept / Approach:
Let original cost price be C. Then original selling price is SP₁ = 1.21C. In the second scenario, new cost price is 0.91C and new selling price is SP₂ = SP₁ - 29. We are told that SP₂ gives 25% profit on 0.91C, so SP₂ = 1.25 * 0.91C. Equating these two expressions for SP₂ gives an equation in C, which we can solve to obtain the original cost price. This structured algebraic approach avoids confusion between the two different profit rates.

Step-by-Step Solution:
Step 1: Let original cost price = C.Step 2: Original selling price SP₁ = 1.21C (because profit is 21%).Step 3: If fruits were bought 9% cheaper, new cost price = 0.91C.Step 4: In the second case, selling price is SP₂ = SP₁ - 29 = 1.21C - 29.Step 5: Given that SP₂ gives 25% profit on 0.91C, so SP₂ = 1.25 * 0.91C = 1.1375C.Step 6: Equate the two expressions: 1.21C - 29 = 1.1375C.Step 7: 1.21C - 1.1375C = 29 ⇒ 0.0725C = 29 ⇒ C = 29 / 0.0725 = 400.

Verification / Alternative check:
Using C = 400, original SP₁ = 1.21 * 400 = Rs 484. New cost price = 0.91 * 400 = Rs 364. New SP₂ = SP₁ - 29 = 484 - 29 = Rs 455. The profit in this second case is 455 - 364 = Rs 91. Profit percentage = (91 / 364) * 100 = 25%. This matches the condition that the second scenario yields a 25% profit, confirming that the original cost price must be Rs 400.

Why Other Options Are Wrong:
If the cost price were Rs 420, 460 or 480, the relationship between selling prices and profit percentages would not match the described conditions. For instance, plugging in 420 would not give the second profit exactly 25% when both the cost and selling price are adjusted as described. Only C = 400 satisfies both the original 21% profit and the modified 25% profit scenario simultaneously.

Common Pitfalls:
Common mistakes include subtracting 9% from the 21% profit directly, or trying to average percentages, which is incorrect here. Another error is forgetting that the Rs 29 difference applies to the selling price, not to the profit. The safest strategy is to always introduce a variable for cost price, write explicit expressions for all relevant selling prices and then carefully equate them using the conditions provided.

Final Answer:
The original cost price of the fruits is Rs. 400.