Question

A precious stone worth Rs $6800$ is accidently dropped and breaks into three pieces The weight of three pieces are in the ratio $5:7:8$. The value of the stone is proportional to the square of its weight. Find the loss

• A. Rs $4260$
• B. Rs $4273$
• C. Rs $4454$
• D. Rs $3250$

Answer 1

Answer: (C)

Rs $4454$

Let the weight of the stone=x

Then, by the given condition,

$6800=k{x}^2$.....(i).

The stone is broken in the ratio 5:7:8 by weight.

So, the weight of the first part=$\frac{5x}{5+6+7}=\frac{5x}{20}$,

the weight of the second part=$\frac{7x}{5+6+7}=\frac{7x}{20}$,

the weight of the third part=$\frac{8x}{5+6+7}=\frac{8x}{20}$,

$\therefore$ The price of the first part=$k{\left(\frac{5x}{20}\right)}^2=\frac{25}{400}{kx}^2$,

the price of the secon part=$k{\left(\frac{k}{7x}20\right)}^2=\frac{49}{400}{kx}^2$,

the price of the third part=$k{\left(\frac{8x}{20}\right)}^2=\frac{64}{400}{kx}^2$.

$\therefore$ The total of the new prices

=$\frac{138}{400}k{x}^2.$

=$Rs\frac{138}{400}\times 6800=Rs2346$ (from i)

$\therefore$ The loss=Rs6800-Rs2346=Rs4454.

Ans- Option C.