The selling price of a fan is Rs 4644 and on this sale the seller earns a profit of 29% on the cost price. What is the cost price of the fan (in rupees)?

Introduction / Context:
This question tests the ability to compute cost price when selling price and profit percentage are given. It is a direct reverse percentage problem that appears regularly in basic profit and loss sections of aptitude exams. Understanding how to express selling price in terms of cost price and profit percentage is the key to solving such questions quickly.

Given Data / Assumptions:

• Selling price SP = Rs 4644.
• Profit percentage on cost price = 29%.
• Cost price CP is unknown and needs to be determined.
• Profit is calculated as SP - CP.

Concept / Approach:
If profit percentage is p, then selling price is equal to (100 + p)% of the cost price. In this question, SP = 129% of CP. Therefore CP can be obtained by dividing SP by 1.29. Once CP is calculated, we can check that adding 29% of CP does indeed yield the given selling price. This simple ratio relationship is a standard approach for these kinds of problems.

Step-by-Step Solution:
Step 1: Let CP be the cost price.Step 2: Profit percentage is 29%, so SP = 129% of CP = 1.29 * CP.Step 3: Given SP = 4644.Step 4: Therefore 1.29 * CP = 4644.Step 5: CP = 4644 / 1.29.Step 6: Compute CP: 4644 / 1.29 = 3600.Step 7: Hence the cost price of the fan is Rs 3600.

Verification / Alternative check:
We can verify by recomputing the selling price from the cost price. If CP = 3600, then profit at 29% is 0.29 * 3600 = 1044. New SP should be CP + profit = 3600 + 1044 = 4644, which exactly matches the given selling price. This confirms that our calculated cost price is correct and that we have used the percentage relation properly.

Why Other Options Are Wrong:
Option A (5900), option B (3500) and option C (3800) do not satisfy the condition that 29% of CP added to CP equals 4644. For example, 29% of 3500 is 1015, giving an SP of 4515, not 4644. Similarly, 29% of 3800 is 1102, giving 4902, which also does not match. Only option D, 3600, fits exactly with the given selling price and profit percentage.

Common Pitfalls:
Some learners mistakenly treat 29% of the selling price as the profit instead of 29% of the cost price, which gives incorrect results. Others subtract 29 from 4644 or perform other unrelated operations. Always remember that profit or loss percentage is based on cost price unless explicitly stated otherwise. Writing SP = (100 + p)% of CP is a good habit to avoid confusion.

Final Answer:
The cost price of the fan is Rs 3600.