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 : 3 : 4 : 5. if the loss in the total value of the diamond was Rs. 118,000. The price of the original diamond was?Solution
Let the weight of the pieces of diamond be x, 3x, 4x, 5x Total weight of diamond = x + 3x + 4x + 5x = 13x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(13x)2 Price of pieces = (kx2 + 9kx2 + 16kx2 + 25kx2) = 51kx2 Loss in price = 169kx2 – 51kx2 = 118kx2 which is given as 118,000 => 118kx2 = 118000 => kx2 = 1000 Original price = 169kx2 = 169 x 1000 = 169000
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