SSC CGL Model Paper 18

Let the weight of diamond = x
The original price of the diamond is proportional to ${\mathit{x}}^2$.
When diamond breaks into three pieces 3y , 5y and 7y .
$\mathit{x}=3\mathit{y}+5\mathit{y}+7\mathit{y}=15\mathit{y}$
Original price of diamond $={\left(15\mathit{y}\right)}^2=225{\mathit{y}}^2$
Price of diamond after breakage $={\left(3\mathit{y}\right)}^2+{\left(5\mathit{y}\right)}^2+{\left(7\mathit{y}\right)}^2=83{\mathit{y}}^2$
According to the question,
$225{\mathit{y}}^2-83{\mathit{y}}^2=42600$
⇒ $142{\mathit{y}}^2=42600$
∴ ${\mathit{y}}^2=300$
Original price of diamond $=225\times 300=\mathrm{₹}67500$