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Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :
- a)100000
- b)140000
- c)150000
- d)175000
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Cost of a diamond varies directly as the square of its weight. A diam...
Broken diamond value = ( 1 + 4 + 9 +16 ) = 30 unit
Actual value of diamond ( 1 + 2 + 3 + 4 )2 = 100 unit
difference (70 units) --> 70,000
100 units = 70,000/70 × 100
= 100,000
Most Upvoted Answer
Cost of a diamond varies directly as the square of its weight. A diam...
Given information:
- Cost of a diamond varies directly as the square of its weight.
- A diamond broke into four pieces with their weights in the ratio 1:2:3:4.
- The loss in the total value of the diamond was 70000.
To find:
The price of the original diamond.
Assumptions:
Let the weight of the original diamond be 'x' and its price be 'y'.
Solution:
Step 1: Determine the weights:
Let the weights of the four pieces be 'w1', 'w2', 'w3', and 'w4', respectively.
According to the given ratio, we can write:
w1 : w2 : w3 : w4 = 1 : 2 : 3 : 4
Step 2: Calculate the weights:
Since the weights are in the ratio 1:2:3:4, we can assume them as:
w1 = x/10, w2 = 2x/10, w3 = 3x/10, w4 = 4x/10
Step 3: Calculate the loss in value:
The loss in the total value of the diamond is given as 70000.
We know that the cost of a diamond varies directly as the square of its weight.
So, the loss in value will also vary directly as the square of the weight.
Since the weights are in the ratio 1:2:3:4, the loss in value will be in the ratio:
(1^2) : (2^2) : (3^2) : (4^2) = 1 : 4 : 9 : 16
Let the loss in value for each weight be 'l'.
Therefore, we can write the equation as:
l : (4l) : (9l) : (16l) = 1 : 2 : 3 : 4
Step 4: Calculate the loss in value:
From the given information, we know that the loss in value is 70000.
So, we can write the equation as:
1l + 2l + 3l + 4l = 70000
10l = 70000
l = 7000
Step 5: Calculate the price of the original diamond:
The price of the original diamond (y) is directly proportional to the square of its weight (x^2).
Therefore, we can write the equation as:
x^2/y = 7000
Since the weights of the four pieces are in the ratio 1:2:3:4, we can write:
(x/10)^2 : (2x/10)^2 : (3x/10)^2 : (4x/10)^2 = 1 : 2 : 3 : 4
Simplifying the equation, we get:
x^2/100 : (2x)^2/100 : (3x)^2/100 : (4x)^2/100 = 1 : 2 : 3 : 4
x^2/100 : 4x^2/100 : 9x^2/100 : 16x^2/100 = 1 :
- Cost of a diamond varies directly as the square of its weight.
- A diamond broke into four pieces with their weights in the ratio 1:2:3:4.
- The loss in the total value of the diamond was 70000.
To find:
The price of the original diamond.
Assumptions:
Let the weight of the original diamond be 'x' and its price be 'y'.
Solution:
Step 1: Determine the weights:
Let the weights of the four pieces be 'w1', 'w2', 'w3', and 'w4', respectively.
According to the given ratio, we can write:
w1 : w2 : w3 : w4 = 1 : 2 : 3 : 4
Step 2: Calculate the weights:
Since the weights are in the ratio 1:2:3:4, we can assume them as:
w1 = x/10, w2 = 2x/10, w3 = 3x/10, w4 = 4x/10
Step 3: Calculate the loss in value:
The loss in the total value of the diamond is given as 70000.
We know that the cost of a diamond varies directly as the square of its weight.
So, the loss in value will also vary directly as the square of the weight.
Since the weights are in the ratio 1:2:3:4, the loss in value will be in the ratio:
(1^2) : (2^2) : (3^2) : (4^2) = 1 : 4 : 9 : 16
Let the loss in value for each weight be 'l'.
Therefore, we can write the equation as:
l : (4l) : (9l) : (16l) = 1 : 2 : 3 : 4
Step 4: Calculate the loss in value:
From the given information, we know that the loss in value is 70000.
So, we can write the equation as:
1l + 2l + 3l + 4l = 70000
10l = 70000
l = 7000
Step 5: Calculate the price of the original diamond:
The price of the original diamond (y) is directly proportional to the square of its weight (x^2).
Therefore, we can write the equation as:
x^2/y = 7000
Since the weights of the four pieces are in the ratio 1:2:3:4, we can write:
(x/10)^2 : (2x/10)^2 : (3x/10)^2 : (4x/10)^2 = 1 : 2 : 3 : 4
Simplifying the equation, we get:
x^2/100 : (2x)^2/100 : (3x)^2/100 : (4x)^2/100 = 1 : 2 : 3 : 4
x^2/100 : 4x^2/100 : 9x^2/100 : 16x^2/100 = 1 :
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Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer?
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Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer?.
Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was70000, the price of the original diamond was :a)100000b)140000c)150000d)175000Correct answer is option 'A'. Can you explain this answer?.
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