Multiple choice

A person bought two watches for Rs. 4800 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit he would get Rs. 50 more. The difference of the cost price of the watches was. एक व्यक्ति दो घड़ियाँ 4800 रू. में खरीदता है और पहली को 10% लाभ पर और दूसरी को 20% लाभ पर बेचता है। यदि वह पहली को 20% लाभ पर और दूसरी को 10% लाभ पर बेचे वह 50 रू. अधिक प्राप्त करता। दोनों घड़ियों के क्रय-मूल्य में अन्तर है-.

  1. Rs. 500

  2. Rs. 400

  3. Rs. 250

  4. Rs. 750

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A Correct answer
Explanation

Let the cost prices be x and y, so x + y = 4800. First scenario: profit = 0.10x + 0.20y. Second scenario: profit = 0.20x + 0.10y. Difference = (0.20x + 0.10y) - (0.10x + 0.20y) = 0.10x - 0.10y = 50. This gives x - y = 500. So the difference in cost prices is Rs. 500. The key insight is that swapping profit percentages changes the total profit by 10% of the difference in cost prices.