Question

    The cost of diamond varies directly as the square of its

    weight. A diamond broke into four pieces with weights in the ratio 3 : 4 : 5 : 6. if the loss in the total value of the diamond was Rs. 119,000. 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 3x, 4x, 5x, 6x Total weight of diamond = 3x + 4x + 5x + 6x = 18x Price ∝ (weight)2 => Price = k(weight)2 ; where, K is constant Original price = k(18x)2 Price of pieces = (9kx2 + 16kx2 + 25kx2 + 36kx2) = 86kx2 Loss in price = 324kx2 – 86kx2 = 238kx2 which is given as 119,000 => 238kx2 = 119000 => kx2 = 500 Original price = 324kx2 = 324 x 500 = 162000

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