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The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 ∶ 2 ∶ 3 ∶ 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?
- a)Rs. 100000
- b)Rs. 140000
- c)Rs. 150000
- d)Rs. 175000
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The cost of diamond varies directly as the square of its weight. A dia...
Let the original weight of the diamond was ‘10x’ gm;
Since the diamond broke into four pieces with their weights in the ratio of 1 ∶ 2 ∶ 3 ∶ 4;
∴ Weights of four pieces = x, 2x, 3x & 4x;
Since the cost of diamond varies directly as the square of its weight;
∴ Cost of diamond pieces = x2, 4x2, 9x2 and 16x2
And Cost of original diamond = (10x)2 = 100x2
Since loss in total value of the diamond was Rs. 70000 on cutting;
∴ 100x2 – x2 – 4x2 – 9x2 – 16x2 = 70000
⇒ 70x2 = 70000
⇒ x2 = 10000
⇒ x = 100
∴ Cost of original diamond = 100x2 = Rs. 100000
∴ 100x2 – x2 – 4x2 – 9x2 – 16x2 = 70000
⇒ 70x2 = 70000
⇒ x2 = 10000
⇒ x = 100
∴ Cost of original diamond = 100x2 = Rs. 100000
Most Upvoted Answer
The cost of diamond varies directly as the square of its weight. A dia...
Given information:
- The cost of a diamond varies directly as the square of its weight.
- A diamond broke into four pieces with weights in the ratio of 1:2:3:4.
- The loss in total value of the diamond was Rs. 70000.
Approach:
To find the price of the original diamond, we need to determine the weights of each piece and then calculate the total loss in value. Let's break down the problem into steps:
1. Determine the weights of each piece:
- Let the original weight of the diamond be 'w'.
- The weights of the four pieces will be w/10, 2w/10, 3w/10, and 4w/10 respectively.
- Simplifying, we get the weights as w/10, w/5, 3w/10, and 2w/5 respectively.
2. Calculate the loss in value for each piece:
- The loss in value for each piece can be calculated using the given information that the cost varies directly as the square of the weight.
- Let the price of the original diamond be 'p'.
- The loss in value for each piece will be (p(w/10)^2), (p(w/5)^2), (p(3w/10)^2), and (p(2w/5)^2) respectively.
- Simplifying, we get the loss in value for each piece as pw^2/100, pw^2/25, 9pw^2/100, and 4pw^2/25 respectively.
3. Calculate the total loss in value:
- The total loss in value is given as Rs. 70000.
- Summing up the losses for each piece, we get the equation pw^2/100 + pw^2/25 + 9pw^2/100 + 4pw^2/25 = 70000.
4. Solve the equation to find the price of the original diamond:
- Simplifying the equation, we get (5pw^2 + 20pw^2 + 9pw^2 + 16pw^2)/100 = 70000.
- Combining like terms, we have 50pw^2/100 = 70000.
- Further simplification gives pw^2 = 70000 * 100/50.
- Solving for p, we get p = 70000 * 100/50w^2.
- Since p represents the price of the original diamond, we can conclude that the price of the original diamond is Rs. 100000.
Therefore, the correct answer is option 'A' Rs. 100000.
- The cost of a diamond varies directly as the square of its weight.
- A diamond broke into four pieces with weights in the ratio of 1:2:3:4.
- The loss in total value of the diamond was Rs. 70000.
Approach:
To find the price of the original diamond, we need to determine the weights of each piece and then calculate the total loss in value. Let's break down the problem into steps:
1. Determine the weights of each piece:
- Let the original weight of the diamond be 'w'.
- The weights of the four pieces will be w/10, 2w/10, 3w/10, and 4w/10 respectively.
- Simplifying, we get the weights as w/10, w/5, 3w/10, and 2w/5 respectively.
2. Calculate the loss in value for each piece:
- The loss in value for each piece can be calculated using the given information that the cost varies directly as the square of the weight.
- Let the price of the original diamond be 'p'.
- The loss in value for each piece will be (p(w/10)^2), (p(w/5)^2), (p(3w/10)^2), and (p(2w/5)^2) respectively.
- Simplifying, we get the loss in value for each piece as pw^2/100, pw^2/25, 9pw^2/100, and 4pw^2/25 respectively.
3. Calculate the total loss in value:
- The total loss in value is given as Rs. 70000.
- Summing up the losses for each piece, we get the equation pw^2/100 + pw^2/25 + 9pw^2/100 + 4pw^2/25 = 70000.
4. Solve the equation to find the price of the original diamond:
- Simplifying the equation, we get (5pw^2 + 20pw^2 + 9pw^2 + 16pw^2)/100 = 70000.
- Combining like terms, we have 50pw^2/100 = 70000.
- Further simplification gives pw^2 = 70000 * 100/50.
- Solving for p, we get p = 70000 * 100/50w^2.
- Since p represents the price of the original diamond, we can conclude that the price of the original diamond is Rs. 100000.
Therefore, the correct answer is option 'A' Rs. 100000.
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The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer?
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The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 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. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer?.
The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The cost of diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 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. A diamond broke into four pieces with their weights in the ratio of 1 2 3 4. If the loss in total value of the diamond was Rs. 70000, what was the price of the original diamond?a)Rs. 100000b)Rs. 140000c)Rs. 150000d)Rs. 175000Correct answer is option 'A'. Can you explain this answer?.
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