Question

The cost of diamond varies directly as the square of its weight. A diamond weighting 10 decigrams costs ₹ 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 denote weight
$\therefore C\propto w^2$
$C=k{w}^2$ (k = constant)
$\Rightarrow 8000=k(10{)}^2$
$\Rightarrow$ k =80
10 dgm dividing in 3 : 2

Hence weight of each piece is $\frac{3}{5}$ $\times$ 10 = 6 dgm

$\frac{2}{5}$ $\times$ 10 = 4 dgm

we get 6 dgm : 4 dgm.
$C_1=80(6{)}^2=80\times 36=₹2880$
$C_2=80(4{)}^2=80\times 16=₹1280C_1+C_2=2880+1280=₹4160$

Loss = 8000 - 4160 = ₹ 3840