A shopkeeper mixes rice worth Rs. 36 per kg and Rs. 48 per kg in the ratio 5 : 3 to form a mixture. How many kg of a third variety worth Rs. 60 per kg should be added to 64 kg of this mixture so that by selling the final mixture at 25% profit, he gets a selling price of Rs. 60 per kg?

ATQ, First, find the cost price of the initial mixture. Cost price of mixture = (36 x 5 + 48 x 3) / (5 + 3) = (180 + 144) / 8 = 324 / 8 = Rs. 40.5 per kg Selling price of final mixture = Rs. 60 per kg at 25% profit So, cost price of final mixture = 60 / 1.25 = Rs. 48 per kg Now apply alligation between mixture of Rs. 40.5 and third variety of Rs. 60 to get mean price Rs. 48: Ratio = (60 - 48) : (48 - 40.5) = 12 : 7.5 = 8 : 5 Thus, initial mixture : third variety = 8 : 5 Given initial mixture = 64 kg = 8 parts So, 1 part = 64 / 8 = 8 kg Third variety = 5 parts = 5 x 8 = 40 kg Hence, the correct answer is 40 kg.