Question
A trader mixes 48 kg of rice costing Rs. 35 per kg with
32 kg of rice costing Rs. 50 per kg. How much rice costing Rs. 65 per kg should be added to the mixture so that, by selling the final mixture at 20% profit, the selling price becomes Rs. 54 per kg?Solution
ATQ, Selling price of final mixture = Rs. 54 per kg Profit = 20% So, cost price of final mixture = 54 / 1.20 = Rs. 45 per kg Now, cost price of original mixture: Total cost = 48 × 35 + 32 × 50 = 1680 + 1600 = 3280 Total quantity = 48 + 32 = 80 kg Mean price = 3280 / 80 = Rs. 41 per kg Now mix rice of Rs. 41 and Rs. 65 to get mean Rs. 45 By alligation: Original mixture : New rice = (65 - 45) : (45 - 41) = 20 : 4 = 5 : 1 If 5 parts = 80 kg, then 1 part = 16 kg Hence, the quantity of rice added = 16 kg.
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