Multiple choice

A man buys 35 kg of sugar and sets a marked price in order to make 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

  1. 31

  2. 22

  3. 35

  4. 25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = 35 * C. Total revenue target = 35 * C * 1.15 = 40.25C. Revenue from first 5 kg = 5 * 1.2C = 6C. Revenue from next 15 kg = 15 * 1.2C * 0.9 = 16.2C. Remaining sugar = 35 - 5 - 15 - 3 = 12 kg. Revenue needed = 40.25C - 6C - 16.2C = 18.05C. Selling price per kg = 18.05C / 12 = 1.504C. Marked price was 1.2C. Increase = (1.504 - 1.2) / 1.2 = 0.253, which is 25%.

AI explanation

Assume the cost price is 100 rupees per kg, making the total cost 3500 rupees, and the marked price is set at 120 rupees per kg to yield a 20 percent profit. He sells 5 kg at 120 rupees, 15 kg at a 10 percent discount for 108 rupees per kg, wastes 3 kg, and must sell the remaining 12 kg at a new marked price to achieve an overall profit of 15 percent on the total cost, which is a total revenue of 4025 rupees. The revenue required from the final 12 kg is 4025 - (600 + 1620) = 1805 rupees, requiring a price of about 150.42 rupees per kg. Since the original marked price was 120 rupees, the percentage increase is ((150.42 - 120) / 120) * 100, which is approximately 25.3 percent. The result is p is nearest to 25.

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