The difference between the cost price and the selling price of an article is Rs 221, and the profit percentage on cost price is 17%.\nWhat is the selling price (in rupees) of the article?

Introduction / Context:
This question is a direct application of the relationship between cost price, profit, and selling price. Knowing the profit percentage and the monetary profit allows us to find the cost price, from which we can compute the selling price. Such questions are fundamental in the profit and loss chapter of quantitative aptitude and help build intuition about how percentage profit relates to actual amounts.

Given Data / Assumptions:

• Difference between selling price (SP) and cost price (CP) is Rs 221.
• This difference represents profit, because the profit percentage is positive.
• Profit percentage on cost price = 17%.
• We must find the selling price SP.
• All amounts and percentages follow standard definitions of profit and cost.

Concept / Approach:
Profit is defined as SP minus CP. Profit percentage is profit divided by cost price multiplied by 100. Here, we know the profit amount and the profit percent, so we can set up the equation 17% of CP = 221 and solve for CP. After finding CP, we add the profit to obtain SP. This stepwise method uses the basic formulas of profit and loss and avoids confusion between percentage profit on cost and on selling price.

Step-by-Step Solution:
Step 1: Let cost price be CP. Step 2: Profit = SP - CP. Given that this difference is Rs 221. Step 3: Profit percentage is 17% of CP, so profit = 17 / 100 * CP. Step 4: According to the problem, 17 / 100 * CP = 221. Step 5: Solve for CP: CP = 221 * 100 / 17. Step 6: Compute 221 * 100 / 17. Since 221 / 17 = 13, CP = 13 * 100 = 1300. Step 7: Selling price SP = CP + profit = 1300 + 221 = 1521. Step 8: Therefore the selling price of the article is Rs 1521.

Verification / Alternative check:
Check the profit percentage using the computed values. Profit = SP - CP = 1521 - 1300 = 221. Profit percentage on cost is 221 / 1300 * 100. Compute 221 / 1300 = 0.17, and multiplying by 100 gives 17%, which matches the given profit rate. This confirms that CP and SP have been calculated correctly and that the selling price is indeed Rs 1521.

Why Other Options Are Wrong:
If SP were Rs 1079, then profit would be negative relative to any reasonable cost, which contradicts the given profit percentage. For SP = Rs 1300, the profit would be zero, not Rs 221. If SP were Rs 1724, then the profit would be 1724 minus CP, and it would not equal 221 when the profit percentage is fixed at 17%. Only the SP value of Rs 1521 leads to a profit of Rs 221 and a profit percentage of exactly 17% on the cost price.

Common Pitfalls:
One error is to treat 221 as 17% of the selling price instead of the cost price. This leads to a different equation and an incorrect answer. Another mistake is to forget that profit percentage uses cost price in the denominator in most standard questions unless otherwise specified. To avoid confusion, always write the formula profit percent = profit / cost price * 100 and substitute the known values carefully.

Final Answer:
The selling price of the article is Rs 1521.