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Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage?
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Price of a diamond is directly proportional to the square of its weigh...
Price of Diamond and Breakage
Price of Diamond
The price of a diamond is directly proportional to the square of its weight. This means that if the weight of a diamond is doubled, the price of the diamond will be quadrupled.
Breakage of Diamond
When a diamond breaks into two pieces, the weights of the two pieces will be in a fixed ratio. For example, if a diamond breaks into two pieces whose weights are in the ratio of 2:3, then the weight of one piece will be twice the weight of the other piece.
Profit or Loss due to Breakage
To calculate the profit or loss due to breakage, we need to first understand how the price of the diamond is affected by the breakage.
Let us assume that the original weight of the diamond was W and the price of the diamond was P.
According to the given information, the price of the diamond is directly proportional to the square of its weight. This can be expressed as:
P = k * W^2
Where k is a constant of proportionality.
Now, let us assume that the diamond breaks into two pieces whose weights are in the ratio of 2:3. This means that the weight of one piece is 2x and the weight of the other piece is 3x, where x is a constant.
Therefore, the original weight of the diamond can be expressed as:
W = 2x + 3x = 5x
The weights of the two pieces are in the ratio of 2:3, which means that:
Weight of one piece = 2x
Weight of other piece = 3x
Now, let us calculate the price of the two pieces.
Price of one piece = k * (2x)^2 = 4kx^2
Price of other piece = k * (3x)^2 = 9kx^2
The total price of the diamond before it broke can be expressed as:
Total Price = P = k * W^2 = k * (5x)^2 = 25kx^2
The total price of the diamond after it broke can be expressed as:
Total Price = Price of one piece + Price of other piece
Total Price = 4kx^2 + 9kx^2 = 13kx^2
The percentage change in the price of the diamond due to breakage can be expressed as:
Percentage Change = ((Total Price before breakage - Total Price after breakage)/Total Price before breakage) * 100
Substituting the values, we get:
Percentage Change = ((25kx^2 - 13kx^2)/25kx^2) * 100 = 48%
Therefore, the percentage profit or loss due
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Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage?
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Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage?.
Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Price of a diamond is directly proportional to the square of its weight. If the diamond breaks into two pieces whose weights are in the ratio of 2:3, then what is the % profit or loss due to breakage?.
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