A shop keeper bought 30 kg. of wheat at the rate of Rs.45 per kg. He sold 40% of the total quantity at the rate of Rs.50 per kg. Approximately, at what price per kg should he sell the remaining quantity to make 25% overall profit?a.Rs.56b.Rs.50c.Rs.60d.Rs.54
Question
A shop keeper bought 30 kg. of wheat at the rate of Rs.45 per kg. He sold 40% of the total quantity at the rate of Rs.50 per kg. Approximately, at what price per kg should he sell the remaining quantity to make 25% overall profit?a.Rs.56b.Rs.50c.Rs.60d.Rs.54
Solution
Step 1: Calculate the total cost of the wheat
The shopkeeper bought 30 kg of wheat at Rs.45 per kg. So, the total cost = 30 kg * Rs.45/kg = Rs.1350
Step 2: Calculate the selling price of the 40% of wheat
40% of the total quantity = 40/100 * 30 kg = 12 kg He sold this at Rs.50 per kg. So, the total selling price = 12 kg * Rs.50/kg = Rs.600
Step 3: Calculate the overall profit
The shopkeeper wants to make a 25% overall profit. So, the total selling price should be = 100% + 25% = 125% of the total cost So, the total selling price should be = 125/100 * Rs.1350 = Rs.1687.5
Step 4: Calculate the selling price of the remaining wheat
The remaining quantity of wheat = 30 kg - 12 kg = 18 kg The selling price of this wheat should be = Total selling price - Selling price of the 40% wheat So, the selling price of the remaining wheat = Rs.1687.5 - Rs.600 = Rs.1087.5
Step 5: Calculate the price per kg of the remaining wheat
The price per kg = Selling price / Quantity So, the price per kg = Rs.1087.5 / 18 kg = Rs.60.42
So, the shopkeeper should sell the remaining quantity of wheat at approximately Rs.60 per kg to make a 25% overall profit. So, the answer is (c) Rs.60.
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