The cost of 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 Rs. 70000, what was the price of the original diamond? 

The cost of 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 Rs. 70000, what was the price of the original diamond?  Correct Answer Rs. 100000

Let the original weight of the diamond was ‘10x’ gm;

Since the diamond broke into four pieces with their weights in the ratio of 1 ∶ 2 ∶ 3 ∶ 4;

∴ Weights of four pieces = x, 2x, 3x & 4x;

Since the cost of diamond varies directly as the square of its weight;

∴ Cost of diamond pieces = x², 4x², 9x² and 16x²

And Cost of original diamond = (10x)² = 100x²

Since loss in total value of the diamond was Rs. 70000 on cutting;

∴ 100x² – x² – 4x² – 9x² – 16x² = 70000

⇒ 70x² = 70000

⇒ x² = 1000

∴ Cost of original diamond = 100x² = Rs. 100000