A manufacturer gains 10%, a wholesale dealer gains 15% over the manufacturer's price, and a retailer gains 25% over the wholesale price. If the final retail price of a table is Rs. 1265, what was the original cost of production for the manufacturer?

Introduction / Context:
This question involves three successive profit margins: manufacturer to wholesaler, wholesaler to retailer, and retailer to customer. It is a practical scenario showing how cumulative markups affect the final selling price. The task is to work backwards from the retail price to find the original cost of production.

Given Data / Assumptions:

• Manufacturer's gain = 10% over his cost of production.
• Wholesale dealer's gain = 15% over the price paid to the manufacturer.
• Retailer's gain = 25% over the wholesale price.
• Final retail price to the customer = Rs. 1265.
• We must find the manufacturer's cost of production.

Concept / Approach:
Let the manufacturer's cost be M. The manufacturer sells at 1.10M to the wholesaler. The wholesaler applies a 15% margin, so he sells at 1.15 * 1.10M to the retailer. The retailer then adds 25% and sells at 1.25 times that wholesale price. The product of these three markup factors equals the ratio between the retail price and the manufacturer's cost. We equate this compounded price to Rs. 1265 and solve for M.

Step-by-Step Solution:
Step 1: Let manufacturer's cost price be M rupees.Step 2: Manufacturer sells to wholesaler at 1.10M.Step 3: Wholesaler sells to retailer at 1.15 * 1.10M = 1.265M.Step 4: Retailer sells to customer at 1.25 * 1.265M = 1.58125M.Step 5: Final retail price is given as Rs. 1265, so 1.58125M = 1265.Step 6: Therefore M = 1265 / 1.58125.Step 7: Note that 1.58125 * 800 = 1265 exactly, so M = Rs. 800.

Verification / Alternative check:
Manufacturer's cost = Rs. 800. Manufacturer sells at 10% profit: 1.10 * 800 = Rs. 880.Wholesaler sells at 15% profit: 1.15 * 880 = Rs. 1012.Retailer sells at 25% profit: 1.25 * 1012 = Rs. 1265.The chain of markups reproduces the given final price, confirming M = 800.

Why Other Options Are Wrong:
If M were Rs. 750, 850, 900 or 700, the final retail price after applying 10%, 15% and 25% successively would differ from Rs. 1265. Only with M = Rs. 800 does the compounded markup exactly match the given retail price.

Common Pitfalls:
Some learners add the percentages directly (10% + 15% + 25%) and attempt to treat the combined markup as a single percentage, which is incorrect because each percentage is applied on a different base. Others may work backwards incorrectly by subtracting 25%, 15% and 10% sequentially without using the proper division by the corresponding factors. Using multiplication and division by accurate decimal factors is the correct approach.

Final Answer:
The manufacturer's original cost of production for the table was Rs. 800.