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?
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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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