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The cost of a 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.

  1. Rs. $1.4$ lakh
  2. Rs. $2.0$ lakh
  3. Rs. $1.0$ lakh
  4. Rs. $2.1$ lakh
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Let 'C' be the cost of original diamond and its weight 'w'

C = k.w2   .... (given)

Now, w1 : w2 : w3 : w4 = 1x : 2x : 3x : 4x

w = w1 + w2 + w3 + w4 = 10x

From the given condition,

k.(10x)2 = k.(1x)2 + k.(2x)2 + k.(3x)2 + k.(4x)2 + 70000

k.100x2 = k.30x2 + 70000

k.x2 = 1000

So the original cost of diamond is k.(10x)2 = 100000 = Rs. 1.0 lakh

C is the answer.

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