Question

the cost of diamond varies directly to the square of its weight at that time the cost of diamond is rupees 7500 and the weight is 50 and mgs.if the Diamond break such that weight of its pieces in the ratio 3 ratio 2 what will be the reduction in the cost of diamond

Answer 1

total reduction is 3600

Answer 2

The reduction in price will be by Rs. 4500

Step-by-step explanation:

Let the weight of the diamond is W and its price is P.

So, given the condition as P ∝ W²

⇒ P = KW² {Where K is a constant of proportionality} ......... (1)

Now, given that when W = 50 mg, then P is 7500 Rs.

So, from equation (1) we get,

7500 = K(50)²

⇒ K = 3

Therefore, equation (1) becomes P = 3W² ........... (2)

Now, we break the diamond of weight 50 mg in a 3 : 2 ratio i.e. 30 mg and 20 mg.

So, the total price of those two diamond pieces will be

$P_{1} + P_{2} = 3(30)^{2} + 3(20)^{2} = 3000$ Rs.

Therefore, the reduction in price will be by Rs. (7500 - 3000) = Rs. 4500 (Answer)