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?

By Peyton

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.