A diamond breaks into 3 piece weighing in the ratio 2:3:5.The value of the diamond is proportionate to the square

value-of-the-diamond

#1

A diamond breaks into 3 piece weighing in the ratio 2:3:5.The value of the diamond is proportionate to the square of it’s weight.If the value of original is Rs 20000,find loss due to breakage

Answer:

Let’s say the original was 10 carats, the pieces would be 2 carats, 3 carats and 5 carats, which add to 10. (notice that 10 was chosen specifically because it was the sum of 2+3+5)

“proportionate to the square of it’s weight” for the original is an equation like

V=kw², where k is a constant, w is weight and V is value.

To determine k, we substitute the known values for the unbroken diamond

20,000=k(10)²
20,000=100k
k=20,000÷100=200

So, the equation now becomes V=200w²

Now we substitute the weights of the piece and add up each value.

V(small)=200(2²)=200(4)=800

V(medium)=200(3²)=200(9)=1800

V(large)=200(5²)=200(25)=5000

Adding the values gives you

800+1800+5000=7600

So, the loss from the breakage is 20,000-7600=12,400

Rs 12,400

Notice that the value of a bog diamond is greater than a few smaller diamonds the total the same weight. This makes sense, really big diamonds are rare.