2017 · Q22
The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1: 2: 3: 4. If the loss in total value of the diamond was ₹ 70,000 , what was the price of the original diamond?
Elementary MathematicsRatio and Proportion
- A₹ 1,00,000
- B₹ 1,40,000
- C₹ 1,50,000
- D₹ 1,75,000
Explanation
Let the piece weights be k, 2k, 3k, 4k (sum 10k). Original value ∝ (10k)² = 100k²; broken value ∝ k² + 4k² + 9k² + 16k² = 30k². The loss ∝ 70k² = ₹70,000, so the original price = (100/70) × 70000 = ₹1,00,000: option A.