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? 
    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 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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