Cost of diamond varies as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 : 3 : 4

1 thought on “Cost of diamond varies as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 : 3 : 4”

1. Answer:

   Let, the weights of the four pieces of the diamond x,2x,3x,4x respectively.

   ∴ Total weight of the original diamond=x+2x+3x+4x=10x

   Let, price of the original diamond=k(100x

   2

   ),wherekisconstant

   ∴ Cost of four pieces=k(x

   2

   +4x

   2

   +9x

   2

   +16x

   2

   )

   =k(30x

   2

   )

   Loss in the total value of the diamond,

   k(100x

   2

   )−k(30x

   2

   )=70000

   ⇒k(70x

   2

   )=70000

   ⇒kx

   2

   =Rs.1000

   Hence, price of the original diamond=k(100x

   2

   )

   =1000×100=Rs.100000.

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