Multiple choice

Cost of diamond varies directly as the square of its weight. A diamond is borken into 4 pieces with their weights in the ratio 1:2:3:4. What is the price of the original diamond if the loss in total value of the diamond amounts to Rs. 140000? किसी हीरे का मूल्य उसके भार के वर्ग के अनुक्रमानुपाती है। एक हीरा चार टुकड़ों में इस प्रकार टूटा कि उसके भारों का अनुपात 1 : 2 : 3 : 4 है। यदि टूटने पर हीरे के मूल्य पर 140000 रू. की हानि हुई हो तो बिना टूटे हीरे का मूल्य कितना था?

  1. Rs. 200000

  2. Rs. 225000

  3. Rs. 215000

  4. Rs. 300000
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A Correct answer
Explanation

Since cost varies directly as the square of weight, P = k*w². When the diamond breaks into pieces with weight ratio 1:2:3:4, the total weight remains the same. Sum of squares: 1² + 2² + 3² + 4² = 30 parts, while original is (1+2+3+4)² = 100 parts. Loss is (100-30)/100 = 70% of original price. 70% of P = 140000, so P = 200000.

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