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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 : 7. if the loss in the total value of the diamond was Rs. 90,000. The price of the original diamond was? 
      A Rs 135000 Correct Answer Incorrect Answer
      B Rs 196000 Correct Answer Incorrect Answer
      C Rs 220500 Correct Answer Incorrect Answer
      D Rs 162000 Correct Answer Incorrect Answer
      E Rs 198550 Correct Answer Incorrect Answer

      Solution

      Let the weight of the pieces of diamond be x, 3x, 4x, 7x Total weight of diamond = x + 3x + 4x + 7x = 15x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(15x)2 Price of pieces = (kx2 + 9kx2 + 16kx2 + 49kx2) = 75kx2 Loss in price = 225kx2 – 75kx2 = 150kx2 which is given as 90,000 => 150kx2 = 90000 => kx2 = 600 Original price = 225kx2 = 225 x 600 = 135000

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