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A diamond weighing 35 grams cost Rs. 12250 is cut down into two pieces having weights in the ratio of 5:2. If the price is directly proportional to the square of the weight then find the loss incurred.
Correct answer is '5000'. Can you explain this answer?
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A diamond weighing 35 grams cost Rs. 12250 is cut down into two pieces...
Given Information:
- Weight of the diamond = 35 grams
- Cost of the diamond = Rs. 12250
- Weight ratio of the two pieces = 5:2
Calculating the weights of the two pieces:
Let the weights of the two pieces be 5x and 2x respectively, where x is a constant.
According to the weight ratio, we have:
5x + 2x = 35
7x = 35
x = 5
Therefore, the weights of the two pieces are:
First piece = 5x = 5 * 5 = 25 grams
Second piece = 2x = 2 * 5 = 10 grams
Calculating the prices of the two pieces:
Since the price is directly proportional to the square of the weight, we can use the formula:
Price = k * (weight)^2
Let the constant of proportionality be k.
So, the prices of the two pieces can be calculated as:
Price of the first piece = k * (25)^2
Price of the second piece = k * (10)^2
Using the given information to calculate the constant of proportionality:
We know that the cost of the diamond is Rs. 12250.
Since the cost is directly proportional to the square of the weight, we can write:
12250 = k * (35)^2
12250 = k * 1225
k = 10
Calculating the prices of the two pieces:
Using the value of k, we can calculate the prices of the two pieces as follows:
Price of the first piece = 10 * (25)^2 = 6250
Price of the second piece = 10 * (10)^2 = 1000
Calculating the loss incurred:
The loss incurred can be calculated as the difference between the original price and the sum of the prices of the two pieces.
Loss incurred = 12250 - (6250 + 1000) = 5000
Therefore, the loss incurred is Rs. 5000.
- Weight of the diamond = 35 grams
- Cost of the diamond = Rs. 12250
- Weight ratio of the two pieces = 5:2
Calculating the weights of the two pieces:
Let the weights of the two pieces be 5x and 2x respectively, where x is a constant.
According to the weight ratio, we have:
5x + 2x = 35
7x = 35
x = 5
Therefore, the weights of the two pieces are:
First piece = 5x = 5 * 5 = 25 grams
Second piece = 2x = 2 * 5 = 10 grams
Calculating the prices of the two pieces:
Since the price is directly proportional to the square of the weight, we can use the formula:
Price = k * (weight)^2
Let the constant of proportionality be k.
So, the prices of the two pieces can be calculated as:
Price of the first piece = k * (25)^2
Price of the second piece = k * (10)^2
Using the given information to calculate the constant of proportionality:
We know that the cost of the diamond is Rs. 12250.
Since the cost is directly proportional to the square of the weight, we can write:
12250 = k * (35)^2
12250 = k * 1225
k = 10
Calculating the prices of the two pieces:
Using the value of k, we can calculate the prices of the two pieces as follows:
Price of the first piece = 10 * (25)^2 = 6250
Price of the second piece = 10 * (10)^2 = 1000
Calculating the loss incurred:
The loss incurred can be calculated as the difference between the original price and the sum of the prices of the two pieces.
Loss incurred = 12250 - (6250 + 1000) = 5000
Therefore, the loss incurred is Rs. 5000.
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Community Answer
A diamond weighing 35 grams cost Rs. 12250 is cut down into two pieces...
Given
New ratio is 5:2.
The price of diamond before broken is Rs. 12250.
Let the weight of each piece of diamond be 5x and 2x.
Total weight of diamond = 5x + 2x = 7x
Cost of the diamond = (7x)2 = 49x2
Cost of first piece = (5x)2 = 25x2
Cost of second piece = (2x)2 = 4x2
Total cost of diamond after weight = 25x2 + 4x2 = 29x2
New cost = 29x2
According to the question,
49x2 = 12250
x2 = 250
The loss in the price of diamond after broken = 49x2 − 29x2
The required loss = 20x2
= 250 × 20
= Rs. 5000
∴ The loss in the price of diamond after broken is Rs. 5000.
Hence, the correct answer is Rs. 5000.
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A diamond weighing 35 grams cost Rs. 12250 is cut down into two pieces having weights in the ratio of 5:2. If the price is directly proportional to the square of the weight then find the loss incurred.Correct answer is '5000'. Can you explain this answer?
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