Question
The cost of diamond varies directly as the square of its
weight. A diamond broke into four pieces with weights in the ratio 1: 4: 5: 6. if the loss in the total value of the diamond was Rs. 89,000. The price of the original diamond was?Solution
Let the weight of the pieces of diamond be x, 4x, 5x, 6x Total weight of diamond = x + 4x + 5x + 6x = 16x Price prop; (weight) 2 = Price = k(weight) 2 ; where, K is constant Original price = k(16x) 2 Price of pieces = (kx 2 + 16kx 2 + 25kx 2 + 36kx 2 ) = 78kx 2 Loss in price = 256kx 2 78kx 2 = 178kx 2 which is given as 89,000 178kx 2 = 89000 kx 2 = 500 Original price = 256kx 2 = 256 x 500 = 128000
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