Question

A diamond price is proportional to square of its weight it gets broken onto $4$ pices with its weight in the ratio $1:2:3:4$. The total price of diamond after breaking is $70000$ less than the diamond in original.What was the price of the original diamond?

• A. $70,000$
• B. $1,00,000$
• C. $1,40,000$
• D. $noneofthese$

Answer 1

Answer: (B)

$1,00,000$

$Let\text{the weight of the four piece of diamond be x,2x,3x,4x}\text{respectively}$

$\text{The weight of the original diamond =x+2x+3x+4x=10x}$

$\text{Let the price of the original diamond =k}\left(100x^2\right)$

$\cos t\text{of four pieces=k}(x^2+4x^2+9x^2+16x^2)=k\left(30x^2\right)$

$Loss\text{in the total value of the diamond=k}\left(\text{100}{\text{x}}^2\right)-k\left(30x^2\right)=7000$

$\Rightarrow k\left(70x^2\right)=70000$

$\Rightarrow k{x}^2=1000$

$Hence\text{price of the original diamond =k}\left(100x^2\right)$

$=RS100000$