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The cost of a piece of diamond varies with the square of its weight. A diamond of Rs. 5,184 value is cut into 3 pieces whose weights are in the ratio 1 : 2 : 3. Find the loss involved in the cutting.
- a)Rs. 3,068
- b)Rs. 3,008
- c)Rs. 3,175
- d)Rs. 3,168
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The cost of a piece of diamond varies with the square of its weight. A...
Given, the cost of a piece of diamond varies with the square of its weight.
⇒ Price = k × weight2 (k is any constant)
Let the weight of a piece of diamond be ‘6x’.
Then, original price = k (6x)2 = 36kx2
⇒ 36kx2 = 5184 ……… eq(1)
The piece is cut into 3 pieces of weights ratio 1 : 2 : 3.
Now, the new price = k (x2 + (2x)2 + (3x)2) = 14kx2
From eq(1)
New price = (14 × 5184)/36 = 2016.
∴ The loss = 5184 – 2016 = Rs. 3168.
⇒ Price = k × weight2 (k is any constant)
Let the weight of a piece of diamond be ‘6x’.
Then, original price = k (6x)2 = 36kx2
⇒ 36kx2 = 5184 ……… eq(1)
The piece is cut into 3 pieces of weights ratio 1 : 2 : 3.
Now, the new price = k (x2 + (2x)2 + (3x)2) = 14kx2
From eq(1)
New price = (14 × 5184)/36 = 2016.
∴ The loss = 5184 – 2016 = Rs. 3168.
Most Upvoted Answer
The cost of a piece of diamond varies with the square of its weight. A...
Given, the diamond is cut into 3 pieces in the ratio 1:2:3. Let the weights of the 3 pieces be x, 2x, and 3x respectively.
Total weight of the diamond = x + 2x + 3x = 6x
According to the given condition, the cost of the diamond varies with the square of its weight. Therefore, if the weight of the diamond is w, its cost is proportional to w^2.
Let the cost of the original diamond be C.
C ∝ (6x)^2 = 36x^2
Now, the diamond is cut into 3 pieces, which means the total cost of the 3 pieces should be equal to the cost of the original diamond.
Cost of the first piece = (x/6)^2 * C
Cost of the second piece = (2x/6)^2 * C = (x/3)^2 * C
Cost of the third piece = (3x/6)^2 * C = (x/2)^2 * C
Total cost of the 3 pieces = (x/6)^2 * C + (x/3)^2 * C + (x/2)^2 * C
Total cost of the 3 pieces = C * (1/36 + 1/9 + 1/4)
Total cost of the 3 pieces = C * (9/36)
Total cost of the 3 pieces = C/4
Given, the value of the diamond after cutting is Rs. 5,184.
Therefore, C/4 = 5,184
C = 20,736
Now, the cost of the first piece = (x/6)^2 * C = (x^2/36) * C
The cost of the second piece = (x/3)^2 * C = (x^2/9) * C
The cost of the third piece = (x/2)^2 * C = (x^2/4) * C
Total cost of the 3 pieces = (x^2/36) * C + (x^2/9) * C + (x^2/4) * C
Total cost of the 3 pieces = (x^2/36 + x^2/9 + x^2/4) * C
Total cost of the 3 pieces = (14x^2/36) * C
Total cost of the 3 pieces = (14x^2/36) * 20,736
Total cost of the 3 pieces = 8,064x^2
Given, the value of the 3 pieces after cutting is Rs. 5,184.
Therefore, 8,064x^2 = 5,184
x^2 = 5,184/8,064
x^2 = 0.6429
x = √0.6429
x = 0.802
Therefore, the weights of the 3 pieces are x = 0.802, 2x = 1.604, and 3x = 2.406.
Now, the cost of the original diamond was Rs. 20,736.
The cost of the 3 pieces after cutting is Rs. 8,064x^2 = Rs. 4,885
Total weight of the diamond = x + 2x + 3x = 6x
According to the given condition, the cost of the diamond varies with the square of its weight. Therefore, if the weight of the diamond is w, its cost is proportional to w^2.
Let the cost of the original diamond be C.
C ∝ (6x)^2 = 36x^2
Now, the diamond is cut into 3 pieces, which means the total cost of the 3 pieces should be equal to the cost of the original diamond.
Cost of the first piece = (x/6)^2 * C
Cost of the second piece = (2x/6)^2 * C = (x/3)^2 * C
Cost of the third piece = (3x/6)^2 * C = (x/2)^2 * C
Total cost of the 3 pieces = (x/6)^2 * C + (x/3)^2 * C + (x/2)^2 * C
Total cost of the 3 pieces = C * (1/36 + 1/9 + 1/4)
Total cost of the 3 pieces = C * (9/36)
Total cost of the 3 pieces = C/4
Given, the value of the diamond after cutting is Rs. 5,184.
Therefore, C/4 = 5,184
C = 20,736
Now, the cost of the first piece = (x/6)^2 * C = (x^2/36) * C
The cost of the second piece = (x/3)^2 * C = (x^2/9) * C
The cost of the third piece = (x/2)^2 * C = (x^2/4) * C
Total cost of the 3 pieces = (x^2/36) * C + (x^2/9) * C + (x^2/4) * C
Total cost of the 3 pieces = (x^2/36 + x^2/9 + x^2/4) * C
Total cost of the 3 pieces = (14x^2/36) * C
Total cost of the 3 pieces = (14x^2/36) * 20,736
Total cost of the 3 pieces = 8,064x^2
Given, the value of the 3 pieces after cutting is Rs. 5,184.
Therefore, 8,064x^2 = 5,184
x^2 = 5,184/8,064
x^2 = 0.6429
x = √0.6429
x = 0.802
Therefore, the weights of the 3 pieces are x = 0.802, 2x = 1.604, and 3x = 2.406.
Now, the cost of the original diamond was Rs. 20,736.
The cost of the 3 pieces after cutting is Rs. 8,064x^2 = Rs. 4,885
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The cost of a piece of diamond varies with the square of its weight. A diamond of Rs. 5,184 value is cut into 3 pieces whose weights are in the ratio 1 : 2 : 3. Find the loss involved in the cutting.a)Rs. 3,068b)Rs. 3,008c)Rs. 3,175d)Rs. 3,168Correct answer is option 'D'. Can you explain this answer?
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