A seller has 230 kg of mangoes which he purchases at rate of Rs. 10 per kg. 20% of total mangoes were rotten in packaging and thrown away. If seller sold half of the remaining mangoes at the rate of Rs. 20 per kg, then at what price (per kg) should seller sell the remaining mangoes to gain a total profit of 15% on the total quantity seller had initially (in Rs. /kg)?
Question
A seller has 230 kg of mangoes which he purchases at rate of Rs. 10 per kg. 20% of total mangoes were rotten in packaging and thrown away. If seller sold half of the remaining mangoes at the rate of Rs. 20 per kg, then at what price (per kg) should seller sell the remaining mangoes to gain a total profit of 15% on the total quantity seller had initially (in Rs. /kg)?
Solution
To solve this problem, let's break it down step by step:
Step 1: Calculate the total cost of the mangoes purchased. The seller purchased 230 kg of mangoes at a rate of Rs. 10 per kg. Total cost = 230 kg * Rs. 10/kg = Rs. 2300
Step 2: Calculate the quantity of rotten mangoes. 20% of the total mangoes were rotten and thrown away. Quantity of rotten mangoes = 20% of 230 kg = 0.2 * 230 kg = 46 kg
Step 3: Calculate the quantity of remaining mangoes. Quantity of remaining mangoes = Total mangoes - Rotten mangoes Quantity of remaining mangoes = 230 kg - 46 kg = 184 kg
Step 4: Calculate the cost of the remaining mangoes. The seller sold half of the remaining mangoes at a rate of Rs. 20 per kg. Quantity of mangoes sold = 184 kg / 2 = 92 kg Cost of mangoes sold = Quantity of mangoes sold * Rate per kg = 92 kg * Rs. 20/kg = Rs. 1840
Step 5: Calculate the cost of the remaining mangoes after selling half. Cost of remaining mangoes = Total cost - Cost of mangoes sold Cost of remaining mangoes = Rs. 2300 - Rs. 1840 = Rs. 460
Step 6: Calculate the selling price of the remaining mangoes to gain a total profit of 15% on the initial quantity. Total profit = 15% of the total cost = 0.15 * Rs. 2300 = Rs. 345 Selling price of the remaining mangoes = Cost of remaining mangoes + Total profit Selling price of the remaining mangoes = Rs. 460 + Rs. 345 = Rs. 805
Step 7: Calculate the selling price per kg of the remaining mangoes. Selling price per kg = Selling price of the remaining mangoes / Quantity of remaining mangoes Selling price per kg = Rs. 805 / 184 kg ≈ Rs. 4.38/kg
Therefore, the seller should sell the remaining mangoes at a price of approximately Rs. 4.38 per kg to gain a total profit of 15% on the initial quantity.
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