Question

a grocer purchased 200 kg of rice at 25 rupee per kg. He sold 80 kg of it at a gain of 10 percent and 40 kg at a loss of 4 percent. at what rate per kg should he sell the remainder to gain 8 percent on his total investment.

Answer 1

STEP 1: Calculate Cost Price :

Cost Price of 200 kg = 25 x 200 = 5000 rupees.

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STEP 2: Calculate Expected Earning:

Gain = 8% x 5000 = 0.08 x 5000 = 400 rupees

Expected Earnings = 5000 + 400 = 5400 rupees

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STEP 3: Find earnings from the sales of 80kg at 10% gain:

Cost of 80kg = 25 x 80 = 2000 rupees

Gain = 10% of 2000 = 0.1 x 2000 = 200 rupees

Total earnings = 2000 + 200 = 2200 rupees

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STEP 4: Find earnings from the sales of 40kg at 4% loss:

Cost of 40 kg = 25 x 40 = 1000 rupees

Loss = 4% x 1000 = 0.04 x 1000 = 40 rupees

Total Earnings = 1000 - 40 = 960 rupees

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STEP 5: Find remaining rice to sell

Remaining = 200 - 80 - 40 = 80 kg

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STEP 6: Find the remaining of the expected earning:

5400 - 2200 - 960 = 2240 rupees

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STEP 7: Find the rate per kg:

80 kg = 2240 rupees

1 kg = 2240 ÷ 80 = 28 rupees

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Answer: He needs to sell the remaining rice at 28 rupees per kg.