Question

The cost of diamond varies directly as the square of its weight. A diamond weight $10$ grams cost $Rs8,000$. If it breaks into two pieces whose weights are in the ratio $3:2$, then the loss incurred (in rupees)

• A. $3840$
• B. $3960$
• C. $4040$
• D. $4160$

Answer 1

The correct option is A $3840$

Cost of diamond $=k(weight{)}^2$
$8000=k(10{)}^2$
$k=\frac{8000}{100}=80$
Diamond was broke into two pieces = $3x+2x=10$,
$5x=10\Rightarrow x=2$
Ist part: $3x=6$
IInd part: $2x=4$
Ist part; $cost\Rightarrow 80\times 36=2880$
IInd part; $cost\Rightarrow 80\times 16=1280$
Total cost = $2880+1280=4160$
So loss = $8000-4160=3840$