Question

Answer the question step by step.

Answer 1

Answer:

Option(2)

Step-by-step explanation:

Method - 1:

Given : Diamond falls and breaks into pieces in ratio of 2:3:5.

Let the weight of these three pieces be 2x,3x and 5x.

Given,value of Diamond is directly Proportional to Square of its weights.

V ∝ W²

⇒ (V/W²) = Constant

⇒ (V₁/W₁²) = (V₂/W₂²)

⇒ V₂ = (V₁W₂²)/(W₁²)

Loss of value:

$\Longrightarrow \frac{96000[(10x)^2 - [(2x)^2 + (3x)^2 + (5x)^2]}{(10x)^2}$

$\Longrightarrow \frac{96000 * 62x^2}{(10x)^2}$

$\Longrightarrow \frac{96000 * 62}{100}$

$\Longrightarrow \boxed{\textbf 59520}$

$\Longrightarrow 59520$

∴ Loss Incurred = 59520.

Method - 2:

Value of the pieces broken = 2² + 3² + 5² = 38 parts.

Total value = (2 + 3 + 5)² = 100 parts.

Loss = 100 - 38 = 62 parts.

Actual Loss = (62/100) * 96000

                    = 59520

∴ Loss Incurred = 59520.

Hope it helps!

Answer 2

suppose  actual weight = W

and its price would be = kW²         let k = 1 , where k is proportionality constant

                so price = W²

now it get rubbled into ratio 2 : 3 :  5

let those pieces weigh 2x , 3x and 5x

                    ⇒ 2x+3x+5x = W ⇒  10x = W ⇒ x= W/10

so those pieces gonna weigh = 2W/10 , 3W/10 and 5W/10

and therefore there prices would be = 4W²/100  ,  9W²/100 and 25W²/100

total price = 4W²/100 + 9W²/100  + 25W²/100 = 38W²/100

loss in actual price = W² - 38W²/100 = 62W²/100

percentage loss =  loss/actual price  x 100

                            =(62W²/100) / W²  x 100  = 62%