Question

Cost of a diamond varies directly as the square of its weight.A diamond broke into four pieces with their weight in the ratio $1:2:3:4$ If the loss in the total value of the diamond was $Rs.70000$. Find the prices of the original diamond.

• A. $10000Rs$
• B. $100000Rs$
• C. $1000000Rs$
• D. $2000000Rs$

Answer 1

The correct option is B $100000Rs$

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

$\therefore$ Total weight of the original diamond$=x+2x+3x+4x=10x$

Let, price of the original diamond$=k\left(100x^2\right),wherekisconstant$

$\therefore$ Cost of four pieces$=k(x^2+4x^2+9x^2+16x^2)=k\left(30x^2\right)$

Loss in the total value of the diamond,

$k\left(100x^2\right)-k\left(30x^2\right)=70000\Rightarrow k\left(70x^2\right)=70000\Rightarrow k{x}^2=Rs.1000$

Hence, price of the original diamond$=k\left(100x^2\right)=1000\times 100=Rs.100000.$