[Rs.1 lakh] The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four

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The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs.70,000 less. Find the original price of the diamond.

Rs.1.4 lakh

Rs.2 lakh

Rs.1 lakh

Rs.2.5 lakh

Explanation:

Let the original weight of the diamond be 10x. Hence, its original price will be k(100x2 ), where k is a constant. The weights of the pieces after breaking are x, 2x, 3x and 4x. Therefore, their prices will be kx2, 4kx2 , 9kx2 and 16kx2 . So the total price of the pieces = (1 + 4 + 9 + 16) kx2 = 30kx2 .

Hence, the difference in the price of the original diamond and its pieces = 100kx 2 – 30kx 2 = 70kx 2 = 70000. Hence, kx2 = 000 and the original price = 100 kx2= 100 × 1000 = 100000 = Rs.1 lakh.

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