Question

Price of a piece of diamond is Rs. 2000. It is broken into two equal pieces. If price of diamond is directly proportional to the square of its weight, then the amount of loss for breaking into two pieces is

• A. Rs. 500
• B. Rs. 1500
• C. Rs. 2000
• D. Rs. 1000

Answer 1

Answer: (D)

Rs. 1000

Let the weight of diamond$=x$
$\therefore x^2=2000$
After breaking the weight of each piece
$\Rightarrow \frac{x}{2}$
$\therefore \text{New price}={\left(\frac{x}{2}\right)}^2+{\left(\frac{x}{2}\right)}^2$
$\Rightarrow 2{\left(\frac{x}{2}\right)}^2$
$\Rightarrow 2\times \frac{x^2}{4}$
$\Rightarrow \frac{x^2}{2}\Rightarrow \frac{2000}{2}=1000$
$\text{therefore loss of breaking}=2000-1000=1000Rs$
Hence, option 'D' is correct.