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A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage?
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A precious stone worth Rs.15,600 is accidentally dropped and broken in...
Given Information:
- The weight of the precious stone is divided into three pieces in the ratio of 2:3:5.
- The value of the stone varies as the cube of its weight.
- The initial value of the stone is Rs.15,600.
To Find:
- The percentage loss incurred due to the breakage.
Solution:
Step 1: Find the weights of the three pieces.
Let the weights of the three pieces be 2x, 3x, and 5x, respectively.
The sum of these weights is 2x + 3x + 5x = 10x.
Step 2: Calculate the value of each piece.
The value of the stone is directly proportional to the cube of its weight.
So, the values of the three pieces are (2x)^3, (3x)^3, and (5x)^3, respectively.
Step 3: Calculate the total value of the stone.
The total value of the stone is the sum of the values of the three pieces.
Total value = (2x)^3 + (3x)^3 + (5x)^3
Step 4: Calculate the percentage loss.
The percentage loss is given by the formula:
Percentage Loss = (Initial Value - Final Value) / Initial Value * 100
To calculate the percentage loss, we need to find the final value of the stone after it is broken into three pieces.
Step 5: Calculate the final value of the stone.
The final value of the stone is the sum of the values of the three pieces.
Final value = (2x)^3 + (3x)^3 + (5x)^3
Step 6: Calculate the percentage loss.
Percentage Loss = (15600 - Final Value) / 15600 * 100
Step 7: Simplify the equation.
15600 - Final Value = 15600 - [(2x)^3 + (3x)^3 + (5x)^3]
15600 - Final Value = 15600 - [8x^3 + 27x^3 + 125x^3]
15600 - Final Value = 15600 - 160x^3
Step 8: Substitute the value of x.
We can find the value of x by solving the equation 2x + 3x + 5x = 10x = 15600.
Solving for x, we get x = 1560.
Substituting the value of x in the equation, we get:
15600 - Final Value = 15600 - 160(1560)^3
Step 9: Calculate the final value.
Calculate the value of (1560)^3 and substitute it in the equation to find the final value.
Step 10: Calculate the percentage loss.
Substitute the value of the final value in the percentage loss formula to calculate the percentage loss incurred.
Final Answer:
The percentage loss incurred due to the breakage is __%.
- The weight of the precious stone is divided into three pieces in the ratio of 2:3:5.
- The value of the stone varies as the cube of its weight.
- The initial value of the stone is Rs.15,600.
To Find:
- The percentage loss incurred due to the breakage.
Solution:
Step 1: Find the weights of the three pieces.
Let the weights of the three pieces be 2x, 3x, and 5x, respectively.
The sum of these weights is 2x + 3x + 5x = 10x.
Step 2: Calculate the value of each piece.
The value of the stone is directly proportional to the cube of its weight.
So, the values of the three pieces are (2x)^3, (3x)^3, and (5x)^3, respectively.
Step 3: Calculate the total value of the stone.
The total value of the stone is the sum of the values of the three pieces.
Total value = (2x)^3 + (3x)^3 + (5x)^3
Step 4: Calculate the percentage loss.
The percentage loss is given by the formula:
Percentage Loss = (Initial Value - Final Value) / Initial Value * 100
To calculate the percentage loss, we need to find the final value of the stone after it is broken into three pieces.
Step 5: Calculate the final value of the stone.
The final value of the stone is the sum of the values of the three pieces.
Final value = (2x)^3 + (3x)^3 + (5x)^3
Step 6: Calculate the percentage loss.
Percentage Loss = (15600 - Final Value) / 15600 * 100
Step 7: Simplify the equation.
15600 - Final Value = 15600 - [(2x)^3 + (3x)^3 + (5x)^3]
15600 - Final Value = 15600 - [8x^3 + 27x^3 + 125x^3]
15600 - Final Value = 15600 - 160x^3
Step 8: Substitute the value of x.
We can find the value of x by solving the equation 2x + 3x + 5x = 10x = 15600.
Solving for x, we get x = 1560.
Substituting the value of x in the equation, we get:
15600 - Final Value = 15600 - 160(1560)^3
Step 9: Calculate the final value.
Calculate the value of (1560)^3 and substitute it in the equation to find the final value.
Step 10: Calculate the percentage loss.
Substitute the value of the final value in the percentage loss formula to calculate the percentage loss incurred.
Final Answer:
The percentage loss incurred due to the breakage is __%.
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A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage?
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A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage?.
A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A precious stone worth Rs.15,600 is accidentally dropped and broken into three pieces , the weights of which are respectively proportional to 2:3:5. The value of the stone of this variety varies as the cube of its weight. Calculate the percentage loss thus incurred by this breakage?.
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