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A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is?
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A diamond worth 4900 is broken into two pieces whoes weights are in ra...
Problem: A diamond worth 4900 is broken into two pieces whose weights are in ratio 9:5. If the value of the diamond is proportional to the square of its weight, what is the loss incurred due to the breakage?
Solution:
Step 1: Find the weights of the two pieces of diamond
Let the weight of the diamond be x.
According to the problem, the weights of the two pieces are in the ratio 9:5.
So, let the weights of the two pieces be 9k and 5k respectively.
Therefore, we have 9k + 5k = x, which gives us k = x/14.
So, the weights of the two pieces are 9(x/14) and 5(x/14), which simplifies to (9/14)x and (5/14)x respectively.
Step 2: Find the value of the two pieces of diamond
Let the value of the diamond be proportional to the square of its weight.
So, the value of the diamond is kx^2, where k is a constant.
Therefore, the value of the two pieces of diamond are (9/14)^2kx^2 and (5/14)^2kx^2 respectively.
Simplifying these expressions, we get (81/196)kx^2 and (25/196)kx^2 respectively.
Step 3: Find the loss incurred due to the breakage
The total value of the diamond before breakage was kx^2.
The total value of the diamond after breakage is (81/196)kx^2 + (25/196)kx^2 = (106/196)kx^2.
The loss incurred due to the breakage is the difference between the total value before breakage and after breakage, which is given by:
kx^2 - (106/196)kx^2
Simplifying this expression, we get (45/196)kx^2.
Step 4: Find the numerical value of the loss
We know that the diamond is worth 4900.
So, kx^2 = 4900.
Substituting the value of kx^2 in the expression for loss, we get:
(45/196)kx^2 = (45/196) * 4900 = 1125
Therefore, the loss incurred due to the breakage is 1125.
Answer: The loss incurred due to the breakage is 1125.
Solution:
Step 1: Find the weights of the two pieces of diamond
Let the weight of the diamond be x.
According to the problem, the weights of the two pieces are in the ratio 9:5.
So, let the weights of the two pieces be 9k and 5k respectively.
Therefore, we have 9k + 5k = x, which gives us k = x/14.
So, the weights of the two pieces are 9(x/14) and 5(x/14), which simplifies to (9/14)x and (5/14)x respectively.
Step 2: Find the value of the two pieces of diamond
Let the value of the diamond be proportional to the square of its weight.
So, the value of the diamond is kx^2, where k is a constant.
Therefore, the value of the two pieces of diamond are (9/14)^2kx^2 and (5/14)^2kx^2 respectively.
Simplifying these expressions, we get (81/196)kx^2 and (25/196)kx^2 respectively.
Step 3: Find the loss incurred due to the breakage
The total value of the diamond before breakage was kx^2.
The total value of the diamond after breakage is (81/196)kx^2 + (25/196)kx^2 = (106/196)kx^2.
The loss incurred due to the breakage is the difference between the total value before breakage and after breakage, which is given by:
kx^2 - (106/196)kx^2
Simplifying this expression, we get (45/196)kx^2.
Step 4: Find the numerical value of the loss
We know that the diamond is worth 4900.
So, kx^2 = 4900.
Substituting the value of kx^2 in the expression for loss, we get:
(45/196)kx^2 = (45/196) * 4900 = 1125
Therefore, the loss incurred due to the breakage is 1125.
Answer: The loss incurred due to the breakage is 1125.
Community Answer
A diamond worth 4900 is broken into two pieces whoes weights are in ra...
Suppose originally the weight of diamond is 14 grams and it's 4900 so according to question, 4900 = k*14*14 (say this is equation 1).
now the diamond is broken into two pieces of 9gms and 5gms and their worth is x and y respectively. Now according to question, x = k*9*9 (say equation 2) and y = k*5*5 (say equation 3). Now if you divide equation 2 with equation 1, you'll get x = 2025. Divide equation 3 with equation 1, you'll get y= 625. So now total worth of two broken pieces us equal to x+y that is 2650 and the loss is 4900-2650 = 2250.
now the diamond is broken into two pieces of 9gms and 5gms and their worth is x and y respectively. Now according to question, x = k*9*9 (say equation 2) and y = k*5*5 (say equation 3). Now if you divide equation 2 with equation 1, you'll get x = 2025. Divide equation 3 with equation 1, you'll get y= 625. So now total worth of two broken pieces us equal to x+y that is 2650 and the loss is 4900-2650 = 2250.
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A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is?
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A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is?.
A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A diamond worth 4900 is broken into two pieces whoes weights are in ratio 9:5 if the value of the diamond is proportional to the square of it's weight the loss incurred due to the breakage is?.
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