By selling cloth at Rs 9 per metre, a shopkeeper incurs a loss of 10% on the cost price. At what price per metre should the cloth be sold so that the shopkeeper earns a profit of 15% on the cost price?

Introduction / Context:
This question tests the basic connection between cost price, selling price, loss percentage and desired profit percentage. The shopkeeper first sells cloth at a loss, then wants to adjust the selling price to achieve a specific profit. Such questions appear frequently in profit and loss sections of aptitude exams and are straightforward when you correctly derive the cost price first.

Given Data / Assumptions:

• Selling price SP1 = Rs 9 per metre with a loss of 10%.
• Loss of 10% means SP1 is 90% of cost price.
• We need a selling price SP2 giving a 15% profit on cost price.
• All prices refer to one metre of cloth.

Concept / Approach:
Loss or profit percentage is always calculated on the cost price. First we work backwards from the given selling price and loss percentage to find the cost price per metre. Then we apply the required profit percentage to that cost price to determine the new selling price per metre. This two step process, cost reconstruction followed by target profit calculation, is standard in such problems.

Step-by-Step Solution:
Step 1: Let cost price per metre be CP.Step 2: Given a 10% loss, we have SP1 = 90% of CP = 0.90 * CP.Step 3: SP1 is Rs 9, so 0.90 * CP = 9.Step 4: Therefore CP = 9 / 0.90 = 10.Step 5: To earn a profit of 15%, selling price SP2 must be 115% of CP.Step 6: SP2 = 1.15 * CP = 1.15 * 10 = 11.5.Step 7: So the required selling price is Rs 11.50 per metre.

Verification / Alternative check:
If CP is Rs 10 and SP2 is Rs 11.50, then profit per metre is 11.50 - 10 = 1.50 rupees. Profit percentage is (1.50 / 10) * 100 = 15%, which matches the desired rate. Similarly, if SP1 is Rs 9 and CP is Rs 10, then the loss is 10%, which confirms the initial condition. Both checks show the calculations are consistent and the answer is correct.

Why Other Options Are Wrong:
Option A (Rs 11.20), option B (Rs 11.30) and option C (Rs 11.40) all correspond to smaller profits than 15% when compared with the cost price of Rs 10. For example, Rs 11.20 gives a 12% profit and Rs 11.40 gives a 14% profit. Only option D, Rs 11.50, yields exactly 15% profit, so the other options are not acceptable.

Common Pitfalls:
Many learners mistakenly take Rs 9 as the cost price, which leads to incorrect calculations of the new selling price. Another common error is mixing up loss and profit percentages, such as adding or subtracting them directly without recalculating based on the cost price. Always reconstruct the cost price from the given loss or profit information before moving to the next step.

Final Answer:
The cloth should be sold at Rs. 11.50 per metre to earn a 15% profit.