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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 4 : 5 : 6 : 7. if the loss in the total value of the diamond was Rs. 179,000. 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 242000 Correct Answer Incorrect Answer

    Solution

    Let the weight of the pieces of diamond be 4x, 5x, 6x, 7x Total weight of diamond = 4x + 5x + 6x + 7x = 22x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(22x)2 Price of pieces = (16kx2 + 25kx2 + 36kx2 + 49kx2) = 126kx2 Loss in price = 484kx2 – 126kx2 = 358kx2 which is given as 179,000 => 358kx2 = 179000 => kx2 = 500 Original price = 484kx2 = 484 x 500 = 242000

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