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      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 : 6. if the loss in the total value of the diamond was Rs. 100,500. The price of the original diamond was? 
      A Rs 128000 Correct Answer Incorrect Answer
      B Rs 196000 Correct Answer Incorrect Answer
      C Rs 169000 Correct Answer Incorrect Answer
      D Rs 147000 Correct Answer Incorrect Answer
      E Rs 198550 Correct Answer Incorrect Answer

      Solution

      Let the weight of the pieces of diamond be x, 3x, 4x, 6x Total weight of diamond = x + 3x + 4x + 6x = 14x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(14x)2 Price of pieces = (kx2 + 9kx2 + 16kx2 + 36kx2) = 62kx2 Loss in price = 196kx2 – 62kx2 = 134kx2 which is given as 100,500 => 134kx2 = 100500 => kx2 = 750 Original price = 196kx2 = 196 x 750 = 147000

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