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

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 : 5. What is the price of the original diamond if the loss
in the total value of the diamond amounts to Rs 118,000?

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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