Question
The cost of diamond varies directly as the square of its
weight. A diamond broke into four pieces with weights in the ratio 2 : 3 : 5 : 6. if the loss in the total value of the diamond was Rs. 91,000. The price of the original diamond was?Solution
Let the weight of the pieces of diamond be 2x, 3x, 5x, 6x Total weight of diamond = 2x + 3x + 5x + 6x = 16x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(16x)2 Price of pieces = (4kx2 + 9kx2 + 25kx2 + 36kx2) = 74kx2 Loss in price = 256kx2 – 74kx2 = 182kx2 which is given as 91,000 => 182kx2 = 91000 => kx2 = 500 Original price = 256kx2 = 256 x 500 = 128000
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