By selling an article for Rs. 390, a shopkeeper makes a profit of 20% on its cost price. Based on this information, what is the cost price of the article in rupees?

Introduction / Context:
This is a straightforward profit and loss question where the selling price and profit percentage are known and the cost price must be determined. Such questions appear frequently in aptitude tests, bank exams, and other competitive exams to check if the candidate remembers and can apply the basic profit formula. Even though the arithmetic is simple, many students make mistakes by inverting the formula or treating the profit percentage in the wrong way. A clean step-by-step approach avoids those errors.

Given Data / Assumptions:
- Selling price (SP) of the article = Rs. 390. - Profit percentage on cost price = 20%. - We need to find the cost price (CP) of the article. - All prices are in rupees; there are no additional taxes or charges.

Concept / Approach:
When there is a profit of P% on the cost price, the relationship between cost price and selling price is SP = CP * (1 + P/100). Here P = 20, so SP = CP * 1.20. We already know SP (Rs. 390), so we can rearrange the formula to find CP as CP = SP / 1.20. This is a direct substitution problem and is an essential pattern to memorize for quick mental calculations in exams.

Step-by-Step Solution:
Given profit percentage P = 20%, so SP = CP * (1 + 20/100) = CP * 1.20. We know SP = Rs. 390, so write: 390 = 1.20 * CP. Rearrange to get CP: CP = 390 / 1.20. Perform the division: 390 / 1.20 = 390 / (6/5) = 390 * (5/6). Compute: 390 * 5 = 1950; then 1950 / 6 = 325. So, CP = Rs. 325.

Verification / Alternative check:
Check the profit on CP = Rs. 325: 20% of 325 = 0.20 * 325 = 65. Add this profit to CP: 325 + 65 = Rs. 390, which matches the given selling price. Since the computed selling price equals the provided selling price, the cost price of Rs. 325 is verified as correct.

Why Other Options Are Wrong:
- Rs. 370 and Rs. 350 would generate selling prices higher than Rs. 390 if a 20% profit was applied, so they are invalid. - Rs. 300 would give a selling price of 300 * 1.20 = 360, which does not match Rs. 390. - Rs. 320 gives SP = 320 * 1.20 = 384, again not equal to Rs. 390.

Common Pitfalls:
Some students mistakenly calculate CP as SP * 1.20 instead of SP / 1.20, which inverts the relationship and gives a much larger value. Another error is to compute profit as 20% of SP rather than 20% of CP, which is incorrect by definition. Rushing through the fraction 390 / 1.20 without properly simplifying it can also cause calculation errors; converting to 390 * 5 / 6 helps avoid mistakes.

Final Answer:
The cost price of the article is Rs. 325.