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

Correct option is (c) Rs 4454

Let the weight of the stone=x Then, by the given condition,

6800 = kx² .....(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 = \(\frac{8x}{5 + 6 + 7} = \frac{8x}{20}\)

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

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

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

∴ The total of the new prices = \(\frac{138}{400} kx^2\)

\(= Rs \frac{138}{400} \times 6800 \)

= Rs 2346   [from (i)]

∴ The loss = Rs 6800 - Rs 2346 = Rs 4454.