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The price of a diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm?
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The price of a diamond varies according to the square of its weight, T...
Problem Statement: The price of a diamond varies according to the square of its weight, The price of gold is directly proportional to its weight. Three rings of equal weight, each composed of a diamond and gold are priced at a, b, and c. The diamonds in them weigh 3, 4, and 5 gms respectively. What is the value of the diamond of 1 gm?
Solution:
Understanding the problem: To find the value of a diamond of 1 gm, we need to first calculate the value of the diamonds of 3, 4, and 5 gms. Given that the rings are of equal weight, the difference in price between the rings can be attributed to the difference in the weight of the diamonds.
Step 1: Calculate the value of diamonds of 3, 4, and 5 gms
Let the value of diamond of 3 gms be x.
Then, the value of diamond of 4 gms is (4/3)^2 * x = 16/9 * x
And, the value of diamond of 5 gms is (5/3)^2 * x = 25/9 * x
Step 2: Calculate the value of gold in each ring
Since the rings are of equal weight, the difference in price between them can be attributed to the difference in the value of the diamonds. Therefore, the value of gold in each ring is the same.
Let the value of gold in each ring be y.
Step 3: Write equations for the given information
We can write the following equations based on the given information:
a = x + y
b = 16/9 * x + y
c = 25/9 * x + y
Step 4: Solve the equations to find the value of x
Subtracting the first equation from the second, we get:
b - a = 7/9 * x
Subtracting the first equation from the third, we get:
c - a = 22/9 * x
Multiplying the first equation by 22/7 and subtracting it from the second, we get:
(22/7) * (b - a) - (c - a) = 0
Simplifying the above equation, we get:
22/63 * x = y - a
Substituting the value of y - a from the first equation, we get:
22/63 * x = b - 2a + x/3
Simplifying the above equation, we get:
x = 63/11 * (b - 2a)
Step 5: Find the value of diamond of 1 gm
Substituting the value of x in terms of a and b, we get:
x = 63/11 * (b - 2a)
x = 63/11 * (16/9 * x - 4/3 * x)
x = 21/11 * x
Therefore, the value of diamond of 1 gm is 21/11 times the value of diamond of 3 gms.
Conclusion: The value of diamond of 1 gm is 21/11 times the value of diamond of 3 gms
Solution:
Understanding the problem: To find the value of a diamond of 1 gm, we need to first calculate the value of the diamonds of 3, 4, and 5 gms. Given that the rings are of equal weight, the difference in price between the rings can be attributed to the difference in the weight of the diamonds.
Step 1: Calculate the value of diamonds of 3, 4, and 5 gms
Let the value of diamond of 3 gms be x.
Then, the value of diamond of 4 gms is (4/3)^2 * x = 16/9 * x
And, the value of diamond of 5 gms is (5/3)^2 * x = 25/9 * x
Step 2: Calculate the value of gold in each ring
Since the rings are of equal weight, the difference in price between them can be attributed to the difference in the value of the diamonds. Therefore, the value of gold in each ring is the same.
Let the value of gold in each ring be y.
Step 3: Write equations for the given information
We can write the following equations based on the given information:
a = x + y
b = 16/9 * x + y
c = 25/9 * x + y
Step 4: Solve the equations to find the value of x
Subtracting the first equation from the second, we get:
b - a = 7/9 * x
Subtracting the first equation from the third, we get:
c - a = 22/9 * x
Multiplying the first equation by 22/7 and subtracting it from the second, we get:
(22/7) * (b - a) - (c - a) = 0
Simplifying the above equation, we get:
22/63 * x = y - a
Substituting the value of y - a from the first equation, we get:
22/63 * x = b - 2a + x/3
Simplifying the above equation, we get:
x = 63/11 * (b - 2a)
Step 5: Find the value of diamond of 1 gm
Substituting the value of x in terms of a and b, we get:
x = 63/11 * (b - 2a)
x = 63/11 * (16/9 * x - 4/3 * x)
x = 21/11 * x
Therefore, the value of diamond of 1 gm is 21/11 times the value of diamond of 3 gms.
Conclusion: The value of diamond of 1 gm is 21/11 times the value of diamond of 3 gms
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The price of a diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm?
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The price of a diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm? 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 diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The price of a diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm?.
The price of a diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm? 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 diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The price of a diamond varies according to the square of its weight, The price of gole directly proportional to its weight. Three rings of equal weight, each Composed of a diamond and gold are priced at a,b and c. The diamonds in them Neigh 3, 4 and 5 gms respectival What is the value of diamond of 1 gm?.
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