Question

The cost of diamond is proportional to the square of its weight.A diamond broke into 4 pieces in the ratio 1:2:3:4. On selling the pieces, the merchant got ₹35000 less than the original price.Find the original price?

Challenge for those who consider themselves Maths Kings and Queens​

Answer 1

what about this .....

check it

Answer 2

The original price is Rs.50000.

Step-by-step explanation:

The cost of diamond is proportional to the square of its weight.

i.e. $\text{Cost} \propto (\text{Weight})^2$

A diamond broke into 4 pieces in the ratio 1:2:3:4.

Let x be the ratio.

So, total weight of original diamond = 1x + 2x+ 3x + 4x = 10x.

Cost of original diamond is given by,

$C= (10x)^2=100x^2$

Total cost of four broken pieces = $x^2(1 + 4 + 9 + 16) = 30k^2$

On selling the pieces, the merchant got ₹35000 less than the original price.

i.e. $100x^2 - 30x^2 = 35000$

$70x^2 = 35000$

$x^2=\frac{35000}{70}$

$x^2=500$

$x=\sqrt{500}$

Cost of original diamond is

$C=100x^2=100\times 500$

$C=50000$

Therefore, the original price is Rs.50000.

#Learn more

A diamond falls and breaks into pieces whose weights are in ratio 2:3:5.The value of the diamond is directly proportional to the square of its weights. Find the loss incurred , if the actual cost of the diamond is Rs.96000

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