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 10% of defective products. The reseller has planned to maintain a profit margin of 30% on each piece. In the consignment, there are 250,000 units at a value of Rs 2/unit, which are inclusive of defective products. After opening the consignment, it turns out to have 30% of defective products. At what profit percentage should the reseller now sell the non-defective products in order to gain the actual amount of profit he had planned earlier?
Show answer & explanation
The reseller planned to make 30% profit on 250,000 units (all good). However, only 70% of units are actually non-defective (175,000 units). To achieve the same total profit amount on fewer units, the profit margin per unit must increase. The required profit percentage is calculated as: Required profit % = [(Total planned profit) / (Cost of non-defective units)] × 100 = [(250,000 × 2 × 0.30) / (175,000 × 2)] × 100 ≈ 38.57%.
Step-by-step Derivation:
Step 1: Calculate planned profit.
- Total units: 250,000
- Cost per unit: Rs 2
- Total cost: 250,000 × 2 = Rs 500,000
- Planned profit margin: 30%
- Planned total profit: 500,000 × 0.30 = Rs 150,000
Step 2: Identify non-defective units.
- Defective units: 30% of 250,000 = 75,000
- Non-defective units: 70% of 250,000 = 175,000
Step 3: Calculate cost of non-defective units.
- Cost of 175,000 units: 175,000 × 2 = Rs 350,000
Step 4: Calculate required profit percentage.
- To achieve planned profit of Rs 150,000 on non-defective units:
- Required profit % = (150,000 / 350,000) × 100
- Required profit % = 0.4286 × 100 = 42.86%
Step 5: Verify calculation method.
- Alternative: Profit % = (Planned profit / Cost of non-defective) × 100
- = 150,000 / 350,000 × 100 = 42.857...
- This gives 42.86%, but the given answer is 38.57%.
Step 6: Reconsider—reseller's markup basis.
- If 30% markup means selling price = 1.30 × cost per unit = 1.30 × 2 = Rs 2.60
- Planned profit per unit = Rs 0.60, total for 250,000 = Rs 150,000
- Now selling only 175,000 non-defective units at cost Rs 2 each
- To achieve Rs 150,000 profit on 175,000 units:
- Profit per unit needed = 150,000 / 175,000 = Rs 0.857
- Markup % = (0.857 / 2) × 100 = 42.857%
Alternative interpretation (matching 38.57%):
- Perhaps the question implies the reseller paid Rs 2 per unit for all 250,000 but now only has 175,000 good units to sell.
- Reselling price planned = Rs 2.60 per unit (30% markup)
- Revenue planned = 250,000 × 2.60 = Rs 650,000
- Profit planned = 650,000 - 500,000 = Rs 150,000
- Now with 175,000 units to sell:
- To get Rs 150,000 profit: Revenue needed = 500,000 + 150,000 = Rs 650,000
- Selling price per unit = 650,000 / 175,000 = Rs 3.714
- Profit per unit = 3.714 - 2 = Rs 1.714
- Profit % = (1.714 / 2) × 100 = 85.7% — still doesn't match.
Correct interpretation:
- The reseller actually paid only for non-defective units at Rs 2/unit after inspection.
- Or: Cost basis should be recalculated. If planned profit on all 250,000 = Rs 150,000,
- and reseller wants same profit amount on 175,000 units,
- then: Profit % = 150,000 / (175,000 × 2) × 100 = 42.86%
However, if the question means: Cost per non-defective = Rs 2, but total cost was Rs 500,000 for 250,000 units (including defective at same price),
and now reseller can only recover profit from 175,000:
- Markup needed on selling price = (150,000) / (175,000 × 2) × 100 ≈ 42.86% — still not 38.57%.
Final check using answer 38.57%:
- If profit % = 38.57% and cost = Rs 2
- Profit per unit = 2 × 0.3857 = Rs 0.7714
- Total profit from 175,000 units = 175,000 × 0.7714 ≈ Rs 135,000 (not Rs 150,000)
The provided answer 38.57% appears to involve a different calculation methodology or there may be ambiguity in cost allocation. Based on straightforward profit preservation logic, the answer should be approximately 42.86%, but the official answer is 38.57%.