A bag is sold for Rs 230 at a profit of 15%. What would be the selling price of the same bag if the shopkeeper wants to earn a profit of 20% instead?

Introduction / Context:
This profit and loss question checks the ability to back-calculate cost price from a known selling price and profit percentage, and then recalculate a new selling price for a different profit percentage. Such questions are standard in competitive exams and help students understand how profit percentages are applied in commercial situations.

Given Data / Assumptions:
- Selling price with 15% profit = Rs 230. - Required profit for the second case = 20%. - The cost price of the bag remains the same in both cases. - No additional costs or taxes are involved.

Concept / Approach:
We use the relation between cost price, selling price, and profit percent:
selling price = cost price * (100 + profit percent) / 100 To find cost price from a known selling price and profit percent, we reverse the formula:
cost price = selling price * 100 / (100 + profit percent) Once the cost price is known, we use it again to find the new selling price for the desired profit percentage.

Step-by-Step Solution:
Step 1: Let cost price be C. Step 2: With 15% profit, 230 = C * 115 / 100. Step 3: Therefore C = 230 * 100 / 115 = 200. Step 4: For 20% profit, new selling price S = C * 120 / 100. Step 5: So S = 200 * 1.2 = Rs 240.

Verification / Alternative check:
Check the profit in each case. When sold at Rs 230, profit = 230 - 200 = Rs 30, which is 30 / 200 * 100 = 15%. When sold at Rs 240, profit = 40, which is 40 / 200 * 100 = 20%. Both percentages match the question data, so the solution is consistent.

Why Other Options Are Wrong:
Option Rs.250 would give a profit of 50 on a cost of 200, which is 25%, not 20%. Option Rs.205 gives almost no profit above cost price. Option Rs.200 is exactly the cost price and corresponds to zero profit, so it cannot represent 20% profit.

Common Pitfalls:
A common mistake is to increase Rs 230 directly by 5% to move from 15% profit to 20% profit. Profit percentages are always based on cost price, so we must go back to cost price first. Another pitfall is to mix up cost price and selling price in the percentage formula, which gives an incorrect answer.

Final Answer:
The bag should be sold at Rs 240 to earn a profit of 20%.