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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: 4: 5: 6. if the loss in the total value of the diamond was Rs. 89,000. The price of the original diamond was?
      A Rs.118000 Correct Answer Incorrect Answer
      B Rs.168000 Correct Answer Incorrect Answer
      C Rs.148000 Correct Answer Incorrect Answer
      D Rs.108000 Correct Answer Incorrect Answer
      E Rs.128000 Correct Answer Incorrect Answer

      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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