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The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.
Correct answer is '100000'. Can you explain this answer?
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The cost of diamond varies directly as the square of its weight. Once...
Given:
The cost of a diamond varies directly as the square of its weight.
The diamond broke into four pieces with weights in the ratio 1:2:3:4.
The merchant got Rs. 70,000 less when the pieces were sold.
To Find:
The original price of the diamond.
Assumptions:
Let the weights of the four pieces be x, 2x, 3x, and 4x respectively.
Let the original price of the diamond be P.
Solution:
Step 1: Understanding the Relationship between Weight and Cost
According to the given information, the cost of the diamond varies directly as the square of its weight. This can be expressed as:
Cost = k * Weight^2
Step 2: Finding the Constant of Variation (k)
To find the constant of variation (k), we need to use the given information that the merchant got Rs. 70,000 less when the pieces were sold. This means the total cost of the four pieces is Rs. 70,000 less than the original price.
Step 3: Expressing Cost in terms of Weight
Using the relationship between cost and weight, we can express the cost of each piece in terms of its weight:
Cost of piece with weight x = k * x^2
Cost of piece with weight 2x = k * (2x)^2 = k * 4x^2
Cost of piece with weight 3x = k * (3x)^2 = k * 9x^2
Cost of piece with weight 4x = k * (4x)^2 = k * 16x^2
Step 4: Finding the Total Cost of the Four Pieces
The total cost of the four pieces can be expressed as the sum of their individual costs:
Total Cost = k * x^2 + k * 4x^2 + k * 9x^2 + k * 16x^2
Total Cost = k * (x^2 + 4x^2 + 9x^2 + 16x^2)
Total Cost = k * 30x^2
Step 5: Equating the Total Cost with the Original Price
According to the given information, the total cost of the four pieces is Rs. 70,000 less than the original price:
k * 30x^2 = P - 70000
Step 6: Using the Weights of the Four Pieces
We know that the weights of the four pieces are in the ratio 1:2:3:4. Therefore, we can express the total weight (W) as:
W = x + 2x + 3x + 4x = 10x
Step 7: Expressing the Original Price in terms of Weight
Using the relationship between cost and weight, we can express the original price in terms of the total weight:
Original Price (P) = k * W^2
Original Price (P) = k * (10x)^2
Original Price (P) = k * 100x^2
Step 8: Equating the Original Price with the Total Cost
We can
The cost of a diamond varies directly as the square of its weight.
The diamond broke into four pieces with weights in the ratio 1:2:3:4.
The merchant got Rs. 70,000 less when the pieces were sold.
To Find:
The original price of the diamond.
Assumptions:
Let the weights of the four pieces be x, 2x, 3x, and 4x respectively.
Let the original price of the diamond be P.
Solution:
Step 1: Understanding the Relationship between Weight and Cost
According to the given information, the cost of the diamond varies directly as the square of its weight. This can be expressed as:
Cost = k * Weight^2
Step 2: Finding the Constant of Variation (k)
To find the constant of variation (k), we need to use the given information that the merchant got Rs. 70,000 less when the pieces were sold. This means the total cost of the four pieces is Rs. 70,000 less than the original price.
Step 3: Expressing Cost in terms of Weight
Using the relationship between cost and weight, we can express the cost of each piece in terms of its weight:
Cost of piece with weight x = k * x^2
Cost of piece with weight 2x = k * (2x)^2 = k * 4x^2
Cost of piece with weight 3x = k * (3x)^2 = k * 9x^2
Cost of piece with weight 4x = k * (4x)^2 = k * 16x^2
Step 4: Finding the Total Cost of the Four Pieces
The total cost of the four pieces can be expressed as the sum of their individual costs:
Total Cost = k * x^2 + k * 4x^2 + k * 9x^2 + k * 16x^2
Total Cost = k * (x^2 + 4x^2 + 9x^2 + 16x^2)
Total Cost = k * 30x^2
Step 5: Equating the Total Cost with the Original Price
According to the given information, the total cost of the four pieces is Rs. 70,000 less than the original price:
k * 30x^2 = P - 70000
Step 6: Using the Weights of the Four Pieces
We know that the weights of the four pieces are in the ratio 1:2:3:4. Therefore, we can express the total weight (W) as:
W = x + 2x + 3x + 4x = 10x
Step 7: Expressing the Original Price in terms of Weight
Using the relationship between cost and weight, we can express the original price in terms of the total weight:
Original Price (P) = k * W^2
Original Price (P) = k * (10x)^2
Original Price (P) = k * 100x^2
Step 8: Equating the Original Price with the Total Cost
We can
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Community Answer
The cost of diamond varies directly as the square of its weight. Once...
Let the original weight of the diamond be 10x. Hence, its original price will be k(100x2), where k is a constant. The weights of the pieces after breaking are x,2x,3x and 4x. Therefore, their prices will be kx2, 4kx2, 9kx2 and 16kx2. So the total price of the pieces = (1 + 4 + 9 + 16)kx2 = 30kx2
Hence, the difference in the price of the original diamond and its pieces
= 100kx2 − 30kx2 = 70kx2 = 70000. Hence, kx2 = 000 and the original price
= 100kx2 = 100 × 1000 = 100000
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The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer?
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The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer?.
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.Correct answer is '100000'. Can you explain this answer?.
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