A wholesaler sells a jacket to a retailer at a profit of 5%, and the retailer sells it to a customer at a further profit of 10%. If the customer pays Rs 4158 for the jacket, what was the cost price of the jacket for the wholesaler?

Introduction / Context:
This chained profit question involves two levels of selling: from wholesaler to retailer and from retailer to final customer. Each level has its own profit percentage. We are given the final selling price to the customer and must work backwards to find the original cost price for the wholesaler.

Given Data / Assumptions:

• The wholesaler sells the jacket to the retailer at a profit of 5%.
• The retailer sells the jacket to the customer at a profit of 10%.
• The final customer pays Rs 4158.
• There are no extra expenses other than the profit margins specified.
• We need the cost price for the wholesaler.

Concept / Approach:
If CPw is the cost price for the wholesaler, then the wholesaler sells at 1.05 * CPw to the retailer. Let CPr be the cost price for the retailer, so CPr = 1.05 * CPw. The retailer then sells to the final customer at 1.10 * CPr. The final selling price equals 4158. Combining these two multiplicative factors gives the total factor from CPw to final SP as 1.05 * 1.10 = 1.155.

Step-by-Step Solution:
Let CPw = x rupees. Wholesaler sells to retailer at 5% profit: CPr = 1.05x. Retailer sells to customer at 10% profit: SP = 1.10 * CPr = 1.10 * 1.05x = 1.155x. Given SP = 4158, so 1.155x = 4158. Thus x = 4158 / 1.155 = 3600 rupees.

Verification / Alternative check:
With CPw = Rs 3600, wholesaler sells at 5% profit: 3600 * 1.05 = Rs 3780. Retailer sells at 10% profit: 3780 * 1.10 = Rs 4158. This matches the given final price, confirming that the cost price to the wholesaler must be Rs 3600.

Why Other Options Are Wrong:
If CPw were 3500, 3400, or 3300 rupees, multiplying by 1.155 would yield final prices of 4042.5, 3927, and 3811.5 respectively, none of which is 4158. Therefore those options do not satisfy the relation between profits and final selling price.

Common Pitfalls:
Some learners mistakenly add percentages instead of multiplying by successive factors, treating the total profit as 15% of wholesaler cost price directly, which is not correct here because of compounding. Always convert each profit percentage into a multiplicative factor and apply them in sequence.

Final Answer:
The cost price of the jacket for the wholesaler was Rs 3600.