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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 2 : 3 : 4 : 5. if the loss in the total value of the diamond was Rs. 142,000. 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

    Solution

    Let the weight of the pieces of diamond be 2x, 3x, 4x, 5x Total weight of diamond = 2x + 3x + 4x + 5x = 14x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(14x)2 Price of pieces = (4kx2 + 9kx2 + 16kx2 + 25kx2) = 54kx2 Loss in price = 196kx2 – 54kx2 = 142kx2 which is given as 142,000 => 142kx2 = 142000 => kx2 = 1000 Original price = 196kx2 = 196 x 1000 = 196000

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