Question

The cost of a precious stone varies as the cube of its weight. A certain precious stone broke into three pieces whose weighs are in the ratio 1 : 2 : 3, as a result of which its cost reduces by 80280. What was the cost of the stone before breaking ?

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Answer 1

$\color {red}\huge\bold\star\underline\mathcal{Question:-}$ we have to find cost of stone before breaking .... ?

$\huge\underline\blue{\sf Given:}$ cost of stone varies as the cube of its weight .. and after breaking into three pieces its cost reduced by 80280 ...

$\bold{\boxed{\huge{\boxed{\orange{\small{\boxed{\huge{\red{\bold{\:Answer}}}}}}}}}}$

Let After breaking the weight of three parts be :- x , 2x & 3x ..

so, initial Total part = (x+2x+3x) = 6x

so, initial cost of full stone = (6x)³ = 216x³

Now,

After breaking its price become =

$(x)^{3} + (2x)^{3} + (3x)^{3} = 36(x)^{3} \:$

So, Decrease in Price ==

$216(x)^{3} - 36(x)^{3} = 180(x)^{3}$

Value of This is Given :- 80280

And , we have to Find initial Price . That is 216x³ .

So,

$180(x)^{3} = 80280 \\ \\ (x)^{3} = \frac{80280}{180} \\ \\ 216(x)^{3} = 446 \times 216 = 96336$

so, initial price of Precious stone was = $\large\red{\boxed{\sf </strong><strong>Rs.\</strong><strong>:</strong><strong>9</strong><strong>6</strong><strong>3</strong><strong>3</strong><strong>6</strong><strong>}}$

$\huge\underline\mathfrak\green{Hope\:it\:Helps\:You}$

Answer 2

$\huge\tt{AnsweR}$

Let x , 2x , 3x be the weight of three parts after breaking:

$\sf Initial \: total \: part \: = (x + 2x + 3x) = 6x \\ \sf Cost \: of \: full \: stone \: = (6x) {}^{3} = 216x {}^{3} \\ \sf Price \: after \: breaking \: = (x) {}^{3} + (2x) {}^{3} + (3x) {}^{3} = 36(x) {}^{3} \\ \sf Decrease \: in \: price \: = 216(x) {}^{3} - 36(x) {}^{3} = 180(x) {}^{2}$

80280 is the value:

$\sf = 180(x) {}^{3} = 80280 \\ \sf = (x) {}^{3} = \frac{80280}{180} \\ \sf = 216(x) {}^{3} = 446 \times 216 = 96336$

Therefore , 96336 is the initial price of precious stone.