A manufacturer promises his reseller that the consignment of goods will not have more than...
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A manufacturer promises his reseller that the consignment of goods will not have more than 1% of defective products. The reseller has planned to maintain a profit of 30% on each piece. In the consignment, if there are 250,000 units at a value of Rs 2/unit, which are inclusive of defective products. After opening the consignment, it now turns out to have 30% of defective products. After opening the consignment, it now turns out to have 30% of defective products at then non-defective products in order to gain the actual amount of profit he had planned earlier.
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The reseller paid Rs 500,000 for all 250,000 units and needs Rs 650,000 revenue (30% profit). With 30% defective (75,000 units), only 175,000 units are sellable. To earn Rs 650,000 from 175,000 units at Rs 2 cost each, the markup must be: [(650,000/175,000 - 2) / 2] × 100 = 38.57%. This ensures the planned 30% profit is achieved despite the higher-than-expected defect rate.
Step-by-step Derivation:
Step 1: Calculate total cost = 250,000 × Rs 2 = Rs 500,000
Step 2: Calculate planned revenue at 30% profit = 500,000 × 1.30 = Rs 650,000
Step 3: Calculate non-defective units = 250,000 × (1 - 0.30) = 175,000 units
Step 4: Selling price per non-defective unit needed = 650,000 / 175,000 = Rs 3.714/unit
Step 5: Markup percentage = [(3.714 - 2) / 2] × 100 = (1.714 / 2) × 100 = 85.7% markup on cost OR 38.57% markup on selling price
Alternatively: Required markup on selling price = [(3.714/2) - 1] × 100/(3.714/2) = 38.57%