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If the manufacturer gains 10%, the wholesale dealer gains 15% and the retailer gains 25%, then the cost of production of a table, the retail price of which is ₹1,265, will be:
₹632.50
₹834.34
₹800.00
₹814.00
₹800.00
To find the initial cost, divide the final retail price by the product of success multipliers: 1265÷(1.10×1.15×1.25)=1265÷1.58125=800.
Manufacturer gain = 10%, Wholesale dealer gain = 15%, Retailer gain = 25%, Retail price = ₹1,265
Cost×(1+G1)×(1+G2)×(1+G3)=Price
To find the initial cost, divide the final retail price by the product of success multipliers: 1265÷(1.10×1.15×1.25)=1265÷1.58125=800.
Students often add percentages (10+15+25 = 50%) instead of applying them sequentially, which leads to an incorrect calculation of 1.5 instead of 1.58125.
Define the relationship
Let the production cost be C. Each gain is a multiplier applied to the previous price: Manufacturer 1.10, Wholesaler 1.15, Retailer 1.25.
C×1.10×1.15×1.25=1265
Calculate the multiplier product
Multiply the factors together: 1.10×1.15=1.265, then 1.265×1.25=1.58125.
1.265×1.25=1.58125
Isolate the cost variable
Divide the retail price of ₹1,265 by the product 1.58125.
C=1.581251265=800
C is correct because the sequential application of 10%, 15%, and 25% gains on a base cost of ₹800 results in the final retail price of ₹1,265.
This concept of chain multipliers is identical to calculating Compound Interest where the time period is replaced by different dealers.
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