The cost of diamond varies directly as the square of its weight. Once,

Solution:

Let 10w units be the original weight of the diamond.

• The cost of the diamond = \(k*100w^2\) , where k is the proportionality constant

After division the cost of the diamond will be directly proportional to \(w^2\), \(4w^2\), \(9 w^2\), and \(16 w^2\)

• The total cost = \(kw^2 + 4kw^2 + 9kw^2 + 16kw^2 = 30kw^2\)

Now, the difference in values is $ 70000.

• \(100kw^2 – 30kw^2 = 70000\)

o \(kw^2 = \frac{70000}{70} = 1000\)
• The original cost of diamond = \(100*kw^2=100*1000 = $ 100000\)

Hence, the correct answer is Option A.

The equation for the price of the diamond is: C2 = C1 * (W2/W1)^2
Where c2: new cost; c1: previous cost; w2: new weight; w1: previous weight

Let's work backwards, from the smallest diamond and up.

We know the ratio (1:2:3:4) and thus we know the weight of the whole diamond (1+2+3+4=10)

W(diamond a) = w1
W (diamond b) = 2
W (diamond c) = 3
W (diamond d) = 4

W (original diamond) = 10

Define the cost of diamond A (w1) as c

Cost (diamond b) = c * (2/1)^2 = 4c
Cost (diamond c) = c * (3/1)^2 = 9c
Cost (diamond d) = c * (4/1)^2 = 16c
Cost (original diamond) = c * (10/1)^2 = 100c

Cost difference = 70000 = 100c - (1c + 4c + 9c + 16c) = 100c - 30c = 70c
70000 = 70c
1000 = c

Orignal diamond cost = 100c = 100000

(edit: small typo)

1:2:3:4 means weights of new pieces are x, 2x, 3x, 4x
Price = k.(weight)^2

Total weight earlier is x+2x+3x+4x = 10x

So deltaprice = k.100x^2 - k(x^2+4x^2+ 9x^2 + 16x^2)
k*70x^2 = 70000

kx^2 = 1000
Hence A

eakabuah

I totally understand this but my question is why k is not part of the equation at all. Shouldn't it be c = kw^2? Can you please explain how you eliminated k?

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