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The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is
- a)1296000
- b)1944000
- c)972000
- d)1620000
Correct answer is option 'A'. Can you explain this answer?
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The price of a precious stone is directly proportional to the square o...
The price of a precious stone is directly proportional to the square of its weight.”
If W is the weight of the stone and P is the price of that stone, then P = k × W2
For the entire, unbroken stone, the price will be 182 × k = 324 k.
“If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000.”
The minimum profit is achieved when the weights of the broken stones are close to each other, that is, the weights are 3, 4, 5, and 6 units.
In this case the combines worth of the four stones =(32 + 42 + 52 + 62)k = 86k
The maximum profit is achieved when the weights of the broken stones are far from each other, that is, the weights are 1, 2, 3, and 12 units.
In this case the combines worth of the four stones =(12 + 22 + 32 + 122)k = 158k
The difference in the total value = 2,88,000.
158k – 86k = 72k = 2,88,000
k = 4,000
So, the price of the original stone = 324 k = 12,96,000
If W is the weight of the stone and P is the price of that stone, then P = k × W2
For the entire, unbroken stone, the price will be 182 × k = 324 k.
“If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000.”
The minimum profit is achieved when the weights of the broken stones are close to each other, that is, the weights are 3, 4, 5, and 6 units.
In this case the combines worth of the four stones =(32 + 42 + 52 + 62)k = 86k
The maximum profit is achieved when the weights of the broken stones are far from each other, that is, the weights are 1, 2, 3, and 12 units.
In this case the combines worth of the four stones =(12 + 22 + 32 + 122)k = 158k
The difference in the total value = 2,88,000.
158k – 86k = 72k = 2,88,000
k = 4,000
So, the price of the original stone = 324 k = 12,96,000
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The price of a precious stone is directly proportional to the square o...
Understanding the Problem:
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000.
Solution:
Given that the price of a precious stone is directly proportional to the square of its weight, we can represent the price of the original stone as 18^2 = 324 units.
When Sita breaks the stone into four pieces with distinct integer weights, the total price of the four pieces will be the sum of the squares of the weights of the individual pieces.
Let the weights of the four pieces be x, y, z, and w.
The total price of the four pieces = x^2 + y^2 + z^2 + w^2
Since the weights are distinct integers, the smallest possible weights for the four pieces are 1, 2, 3, and 4, and the largest possible weights are 15, 16, 17, and 18.
Therefore, the difference between the highest and lowest possible values of the total price = (15^2 + 16^2 + 17^2 + 18^2) - (1^2 + 2^2 + 3^2 + 4^2) = 1296 - 144 = 1152.
Given that the actual difference is 288000, we need to scale it up by a factor of 250 (288000/1152) to get the actual price of the original stone.
The price of the original precious stone = 324 * 250 = 81000 * 4 = 1296000.
Therefore, the correct answer is option A) 1296000.
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000.
Solution:
Given that the price of a precious stone is directly proportional to the square of its weight, we can represent the price of the original stone as 18^2 = 324 units.
When Sita breaks the stone into four pieces with distinct integer weights, the total price of the four pieces will be the sum of the squares of the weights of the individual pieces.
Let the weights of the four pieces be x, y, z, and w.
The total price of the four pieces = x^2 + y^2 + z^2 + w^2
Since the weights are distinct integers, the smallest possible weights for the four pieces are 1, 2, 3, and 4, and the largest possible weights are 15, 16, 17, and 18.
Therefore, the difference between the highest and lowest possible values of the total price = (15^2 + 16^2 + 17^2 + 18^2) - (1^2 + 2^2 + 3^2 + 4^2) = 1296 - 144 = 1152.
Given that the actual difference is 288000, we need to scale it up by a factor of 250 (288000/1152) to get the actual price of the original stone.
The price of the original precious stone = 324 * 250 = 81000 * 4 = 1296000.
Therefore, the correct answer is option A) 1296000.
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The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone isa)1296000b)1944000c)972000d)1620000Correct answer is option 'A'. Can you explain this answer?
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The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone isa)1296000b)1944000c)972000d)1620000Correct answer is option 'A'. 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 price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone isa)1296000b)1944000c)972000d)1620000Correct answer is option 'A'. 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 price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone isa)1296000b)1944000c)972000d)1620000Correct answer is option 'A'. Can you explain this answer?.
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