Multiple choice

A dishonest and particularly negotiating dealer purchases goods from his wholesaler at 50% discount on the cost price of Rs. x and also cheats his wholesaler by getting 50% extra through false weighing, per kg. Then, he marks up his goods by 80% on the cost price of Rs. x, but he gives a discount of 25%. Besides, he cheats his customer by weighing 50% less than the required weight. What is his overall profit percentage?

  1. 400%

  2. 710%

  3. 305%

  4. 240%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cost price per kg = x. Purchase: 50% discount means cost = 0.5x. False weight: gets 1.5 kg for price of 1 kg, so cost per kg = 0.5x / 1.5 = x/3. Selling: Mark up 80% on x = 1.8x. Discount 25% = 1.8x * 0.75 = 1.35x. False weight: sells 0.5 kg for price of 1 kg, so revenue per kg = 1.35x / 0.5 = 2.7x. Profit = (2.7x - x/3) / (x/3) = (8.1x - x) / x = 7.1 = 710%.

AI explanation

Let the cost price of the goods be Rs. 100 for 1000 grams. The dealer gets a 50% discount, making his purchase price Rs. 50, and he uses false weights to get 50% extra, meaning he receives 1500 grams for Rs. 50. This makes his effective cost price for 1000 grams Rs. 33.33. He marks the price up by 80% to Rs. 180 and gives a 25% discount, so he sells 1000 grams for Rs. 135. However, because he weighs 50% less, he actually gives only 500 grams to the customer while charging the full Rs. 135, meaning his selling price for an original 1000 grams is Rs. 270. Using the overall profit percentage formula, the profit is (270 - 33.33) divided by 33.33 and multiplied by 100, which calculates to 710%.

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