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A lorry load of material of mixed goods was purchased for $ 1,00,000. Later on these were sorted out into the following categories: Category A: 1,000 units - Selling price, $ 20 per unit. Category B : 2,000 units Selling price, $ 22.50 per unit Category C: 2,400 units - Selling price $ 25, per unit. Find out the purchase rate per unit of each category of the material assuming that all grades yield the same rate of profit