Question

The cost of diamond varies directly as the square of its weight. A diamond weighting 10 decigrams costs Rs. 8,000. If it breaks into two pieces whose weights are in the ratio 3:2, then the loss incurred (in rupees) is

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

Answer 1

The correct option is A

3840

Let $C$ denote cost and $w$ denotes the weight of the diamond
$\therefore C\propto w^2$
$C=k{w}^2$ (k = constant)
$\Rightarrow 8000=k(10{)}^2$
$\Rightarrow$ k =80
10 dgm dividing in 3:2 we get 6 dgm:4 dgrm.
$C_1=80(6{)}^2=80\times 36=Rs.2880$
$C_2=80(4{)}^2=80\times 16=Rs.1280C_1+C_2=2880+1280=Rs.4160$

Loss = 8000 - 4160 = Rs. 3840