A trader allows a discount of 15% on a trolley bag whose list price is Rs 1360 and still earns a profit of 15.6%. What is the cost price, in rupees, of the trolley bag?

Introduction / Context:
This question combines the ideas of list price (also called marked price), discount, and profit percentage. The aim is to work backwards from the selling price and known profit to find the original cost price. This type of question is very common in shop or retail based profit and loss problems in aptitude exams.

Given Data / Assumptions:

• List price (marked price) of the trolley bag is Rs 1360.
• Discount offered on the list price is 15%.
• The trader earns a profit of 15.6% on the cost price.
• We are required to find the cost price (CP) of the trolley bag.
• No other expenses or taxes are involved.

Concept / Approach:
First, calculate the selling price (SP) after applying the 15% discount on the list price. Next, relate that selling price to the cost price using the profit percentage: SP = CP * (1 + profit percentage). Rearranging this formula gives CP = SP / (1 + profit percentage). Substituting the numbers yields the original cost price.

Step-by-Step Solution:
List price = Rs 1360. Discount = 15% of 1360 = 0.15 * 1360 = Rs 204. Selling price SP = list price - discount = 1360 - 204 = Rs 1156. Profit percentage = 15.6%, so SP = CP * (1 + 15.6/100) = CP * 1.156. Thus CP = SP / 1.156 = 1156 / 1.156 = Rs 1000.

Verification / Alternative check:
Using CP = Rs 1000, profit at 15.6% is 1000 * 0.156 = Rs 156. Then SP should be 1000 + 156 = Rs 1156. This matches the selling price obtained from applying 15% discount to the list price. Therefore, the cost price of Rs 1000 is consistent from both directions.

Why Other Options Are Wrong:
If CP were Rs 1005 or Rs 1050, then multiplying by 1.156 would give selling prices that are not equal to Rs 1156. Similarly, Rs 1156 as cost price would imply zero discount or incorrect profit calculations. Hence only Rs 1000 correctly satisfies both the given discount and profit data.

Common Pitfalls:
A common mistake is to apply the profit percentage on the list price instead of cost price. Some learners also miscalculate discount and do not correctly subtract it from the list price. Another frequent error is to add instead of dividing by the profit factor when solving for cost price.

Final Answer:
The cost price of the trolley bag is Rs 1000.