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The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.?
Verified Answer
The cost of coal block varies directly with the square of its weight.t...
Cost = (5x)^2 + (6x)^2 + (7x)^2 = 110x^2
When weights equal = (6x)^2 + (6x)^2 + (6x)^2 = 108x^2
Loss = 7200 = 110x^2 - 108x^2 = 2x^2
x = 60
Actual cost = (6x + 6x + 6x)^2
(18 * 60)^2 = 1166400
When weights equal = (6x)^2 + (6x)^2 + (6x)^2 = 108x^2
Loss = 7200 = 110x^2 - 108x^2 = 2x^2
x = 60
Actual cost = (6x + 6x + 6x)^2
(18 * 60)^2 = 1166400
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The cost of coal block varies directly with the square of its weight.t...
Solution:
Given data:
- The cost of coal block varies directly with the square of its weight.
- The coal block is divided into three parts whose weight is in the ratio of 5:6:7.
- The coal block is divided into three equal parts of weight, which results in further loss of 7200.
To find: The actual cost of coal block.
Let us assume that the original weight of the coal block is 'w' and its cost is 'c'. Then we have:
- The weights of the three parts of the coal block are 5w/18, 6w/18, and 7w/18.
- The cost of each part varies directly with the square of its weight. So, the cost of the three parts can be expressed as c1 = k(5w/18)^2, c2 = k(6w/18)^2, and c3 = k(7w/18)^2, where k is a constant of proportionality.
- We can simplify the above equations to c1 = (25k/324)w^2, c2 = (36k/324)w^2, and c3 = (49k/324)w^2.
- Let us assume that each of the three equal parts has weight 'x'. Then we have x = w/3.
- The further loss of 7200 can be expressed as (c1/3) + (c2/3) + (c3/3) - c = 7200, where c is the actual cost of the coal block.
Solving the above equations, we get:
- k = (324c)/(5w^2 + 6w^2 + 7w^2) = (324c)/(18w^2) = 18c/w^2
- (25k/324)x^2 + (36k/324)x^2 + (49k/324)x^2 - c = 7200
- Substituting the value of k from the first equation, we get:
(25*18c/w^2*324)x^2 + (36*18c/w^2*324)x^2 + (49*18c/w^2*324)x^2 - c = 7200
- Simplifying the above equation, we get:
c = 97200w^2/1157
Therefore, the actual cost of the coal block is 97200w^2/1157.
Explanation:
- We have used the concept of direct variation to express the cost of each part of the coal block in terms of its weight.
- We have used the given ratio of weights to find the individual weights of the three parts.
- We have assumed the weight of each equal part to find the further loss in cost.
- We have solved the equations to find the actual cost of the coal block.
- The final answer is expressed in terms of the original weight of the coal block.
Given data:
- The cost of coal block varies directly with the square of its weight.
- The coal block is divided into three parts whose weight is in the ratio of 5:6:7.
- The coal block is divided into three equal parts of weight, which results in further loss of 7200.
To find: The actual cost of coal block.
Let us assume that the original weight of the coal block is 'w' and its cost is 'c'. Then we have:
- The weights of the three parts of the coal block are 5w/18, 6w/18, and 7w/18.
- The cost of each part varies directly with the square of its weight. So, the cost of the three parts can be expressed as c1 = k(5w/18)^2, c2 = k(6w/18)^2, and c3 = k(7w/18)^2, where k is a constant of proportionality.
- We can simplify the above equations to c1 = (25k/324)w^2, c2 = (36k/324)w^2, and c3 = (49k/324)w^2.
- Let us assume that each of the three equal parts has weight 'x'. Then we have x = w/3.
- The further loss of 7200 can be expressed as (c1/3) + (c2/3) + (c3/3) - c = 7200, where c is the actual cost of the coal block.
Solving the above equations, we get:
- k = (324c)/(5w^2 + 6w^2 + 7w^2) = (324c)/(18w^2) = 18c/w^2
- (25k/324)x^2 + (36k/324)x^2 + (49k/324)x^2 - c = 7200
- Substituting the value of k from the first equation, we get:
(25*18c/w^2*324)x^2 + (36*18c/w^2*324)x^2 + (49*18c/w^2*324)x^2 - c = 7200
- Simplifying the above equation, we get:
c = 97200w^2/1157
Therefore, the actual cost of the coal block is 97200w^2/1157.
Explanation:
- We have used the concept of direct variation to express the cost of each part of the coal block in terms of its weight.
- We have used the given ratio of weights to find the individual weights of the three parts.
- We have assumed the weight of each equal part to find the further loss in cost.
- We have solved the equations to find the actual cost of the coal block.
- The final answer is expressed in terms of the original weight of the coal block.
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The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.?
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The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.?.
The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of coal block varies directly with the square of its weight.the coal block is divided into three parts whose weight are In the ratio of 5:6:7.if the coal block is divided into three equal part of weight then there would be further loss of 7200.then what is the actual cost of coal books.?.
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