The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.
Explanation:
Let the original weight of the diamond be 10x. Hence, its original price will be k(100x2) . . . where k is a constant.
The weights of the pieces after breaking are x, 2x, 3x and 4x. Therefore, their prices will be kx2, 4kx2, 9kx2 and 16kx2. So the total price of the pieces = (1 + 4 + 9 + 16)kx2 = 30kx2. Hence, the difference in the price of the original diamond and its pieces = 100kx2 – 30kx2 = 70kx2 = 70000. Hence, kx2 = 1000 and the original price = 100kx2 = 100 × 1000 = 100000 = Rs. 1 lakh.
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