A shopkeeper purchased 15 kg of variety A rice at Rs. X per kg and 10 kg of variety B rice at Rs. (X + 5) per kg. The shopkeeper sold the whole quantity of variety A rice at 10% profit and that of variety B rice at 20% profit. The total selling price of variety A rice was Rs. 30 more than that of variety B rice. Had the two varieties been mixed and sold at an overall profit of 20%, what would have been the selling price (per kg)?
Explanation:
Rice A Rice B
Cost price 15 × x 10 × (x + 5)
↓10% profit ↓20% profit
Selling price 110% of 15x 120% of (10x + 5)
= 16.5x = 12x + 60
Now, 16.5x = 12x + 60 + 30
or, 4.5x = 90
∴ x = 90/4.5 = Rs. 20 kg
Now, new selling price of mixture
= [15 × 20 + 10 (20 + 5)] 120/100 = Rs.600
∴ SP per kg = 600/25 = Rs. 26.4 per kg
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By: Amit Kumar