Given that, the ratio of weights of four pieces $ = \text{P}_{1} : \text{P}_{2} : \text{P}_{3} : \text{P}_{4} : = 1:2:3:4 $
so weights are :
- $\text{P}_{1} = k$
- $\text{P}_{2} = 2k$
- $\text{P}_{3} = 3k$
- $\text{P}_{4} = 4k$
The cost of a diamond varies directly as the square of its weight.
So costs are :
- $\text{P}_{1} = k^{2}$
- $\text{P}_{2} = (2k)^{2} = 4k^{2}$
- $\text{P}_{3} = (3k)^{2} = 9k^{2}$
- $\text{P}_{4} = (4k)^{2} = 16k^{2}$
The weight of original diamond $ = k+2k+3k+4k = 10k$
The cost of original diamond $ = (10k)^{2} = 100k^{2}$
Now, $100k^{2} – (k^{2} + 4k^{2} + 9k^{2} + 16k^{2}) = 70000 $
$\Rightarrow 100k^{2} – 30k^{2} = 70000$
$\Rightarrow 70k^{2} = 70000$
$\Rightarrow \boxed{k^{2} = 1000}$
$\therefore$ The price of original diamond $ = 100k^{2} = 100 \times 1000$
Correct Answer $:100000 =$ ₹ $100000$