a very interesting arithmetic problem .?

Question

the value of a stone is varies with cubic of its weight. the value of a 20 gm stone $10000. if the stone is broken by three parts into 5:3:2 then estimate the loss due to the breakage.

Answer 1

The individual parts weight 10gm, 6 gm and 2 gm which are valued at $1250 $10000*(10gm/20gm)^3], $270 and $80 respectively.

Loss due to breakage = $10000-$(1250+270+80)=$8400

Answer 2

If the original stone is worth $10000 and this equates to it's cubic weight then:

20 x 20 x 20 = $10000
So 8000 = $10000
The three new stones at ratios of 5 ; 3 ; 2 would have volumes of
10 x 10 x 10 = 1000
8 x 8 x 8 = 512
4 x 4 x 4 = 64

Total 1576 which would leave a massive wastage of 8000 - 1576 = 6424

This obviously cannot be right since the problem said that the stone was broken into three parts with ratios of 5,3 and 2 so one must assume the whole volume is used. This would give stones weighing 10 grams, 6 grams and 4 grams but the volumes would be 4000, 2400 and 1600 respectively. Based on this there would be no loss.

Answer 3

original weight was 20 grams

it gets broken in 3 parts, in ratios of 5 units, 3 units, and 2 units. Total, 5 + 3 + 2 = 10 units.

So each unit is 20/10 = 2 grams

So the first stone is 5*2 = 10 grams, the second is 3*2 = 6 grams, the third is 2*2 = 4 grams.

The cubic power of 20 is 20*20*20 = 8'000.

the cubic power of 10 is 10*10*10 = 1'000. Which is 8 times less. So the first broken bit will be worth 10'000/8 = 1'250 dollars.

cubic power of 6 is 216. That's 37x less (rounded) than 20^3, so that stone will be worth just 10'000/37=270 dollars (rounded).

cubic power of 4 is 64. That's 125x less than 20^3. so that 3rd stone will be worth 10'000/125=just 80 dollars.

So the total value of the 3 stones will be 1'250 plus 270 plus 80 dollars = 1'600 dollars. That's 6.25x less than the value of the original stone, although the weight is the same!

The person who broke that stone probably lost their job by now...

Hope this helps

Answer 4

The information that the original stone weighed 20 gms is irrelevant and not needed, i.e. the percentage of the value that is lost is independent of the weight of the stone. The percentage of the value that is lost is also independent of the original value of the stone.

I consider three cases, so as to illustrate the folly of diamond cutting,

(1) If value were proportional to the square of the weight, the answer would be it loses 62% of its value.

(2) As we are dealing with value proportional to the cube of the weight, the answer is it loses 84% of its value.

(3) If value were proportional to the fourth power of the weight, the answer would be it loses 92.78 % of its value.

(These are not estimates, but are exact answers),

i.e.

(1) square of the weight: it loses $6,200 and is now worth $3,800.

We're comparing 10^2 (=100) with 5^2 + 3^2 + 2^2 (=38),

(2) cube of the weight: it loses $8,400 and is now worth $1,600.

We're comparing 10^3 (=1000) with 5^3 + 3^3 + 2^3 (= 125 + 27 + 8 = 160),

(3) fourth power of the weight: it loses $9,278 and is now worth $722.

We're comparing 10^4 (= 10,000) with 5^4 + 3^4 + 2^4 (= 625 + 81 + 16 = 722),

Answer 5

PROFIT RATIO IS ( 5^3 + 3^3 + 2^3)/(5+3+2)^3
ie.(125+27+8)/(10^3)
ie.(160/1000)
=======>loss% =1-(160/1000)
=1-0.16
=0.84
====>loss=0.84x10000$
loss=8400$

Answer 6

$100

Answer 7

The loss due to breakage is $8400.

Answer 8

For the month-to-month charge the formulation is M= p(r/n)(a million+r/12)^12t over (a million+r/12)^12t-a million the place M=the month-to-month charge, p=the finished amnt, r=the share fee as a decimal, and t= the time in years.

Answer 9

Estimate = 20 %

0.20 X $ 10,000 = $ 2,000

Use better cut ratio.