The value of a diamond varies directly with the square of its weight. A diamond is cut into three pieces whose weights are in the ratio 3 : 4 : 5. Consequently, by what percentage does the value of the diamond diminish?
Question
The value of a diamond varies directly with the square of its weight. A diamond is cut into three pieces whose weights are in the ratio 3 : 4 : 5. Consequently, by what percentage does the value of the diamond diminish?
Solution
To solve this problem, we need to understand the relationship between the value of a diamond and its weight. The problem states that the value of a diamond varies directly with the square of its weight. This means that if we double the weight of the diamond, its value will increase by a factor of four (since 2^2 = 4).
The problem also states that a diamond is cut into three pieces whose weights are in the ratio 3 : 4 : 5. This means that the total weight of the diamond is divided into 12 parts (since 3 + 4 + 5 = 12).
Let's assume that the original weight of the diamond is W. Then, the weights of the three pieces are 3W/12, 4W/12, and 5W/12 respectively.
The value of the diamond before it was cut is proportional to the square of its weight, or (W^2).
After the diamond is cut, the total value of the three pieces is proportional to the sum of the squares of their weights, or (3W/12)^2 + (4W/12)^2 + (5W/12)^2.
Simplify this to get 9W^2/144 + 16W^2/144 + 25W^2/144 = 50W^2/144.
The percentage by which the value of the diamond diminishes is given by the difference between the original value and the new value, divided by the original value, times 100%.
So, the percentage diminution in value is ((W^2 - 50W^2/144) / W^2) * 100% = (94/144)*100% = 65.28%.
Therefore, the value of the diamond diminishes by approximately 65.28% when it is cut into three pieces whose weights are in the ratio 3 : 4 : 5.
Similar Questions
A diamond falls and breaks into three pieces whose weights are in the ration 1 : 3 : 6. The value of the diamond is proportional to the square of its weight. If the original value is Rs. 30,000. What is the loss in the value due to the breakage?
Mr Rajveer purchased a unique diamond called "Zoinoor", which was very expensive and the cost of the diamond is proportional to square of its weight. But he accidently broke the diamond and it was split into three pieces which were in ratio of 3:2:1 by weight. If he incurred a total loss of Rs 46200 due to the accident, find the initial cost of diamond.Rs 75600Rs 29400Rs 46200Rs 12000
Under very specific instructions, a jeweller made one ring for the queen and one ring for the princess. The gem on the queen's ring weighed 3 3/4 carats and the stone on the princess's ring weighed 1/8 of a carat. How much heavier was the stone on the queen's ring than the stone on the princess's?Write your answer as a fraction or as a whole or mixed number.
Length, Breadth and Height of a 3D figure is in the ratio 3:2:1. If the length is doubled and Breadth & Height are halved, then what is the % decrease in the volume of the solid?Decreased by 15%Decreased by 18%Decreased by 30%Decreased by 50%
The relation between the weight of a diamond and its cost is linear. In looking at two diamonds, we find that one of the diamonds weighs 0.7 carat and costs $3672, while the other diamond weighs 0.8 carat and costs $4568. Linear function that relates the price of a diamond (P) to its weight (x) is P(X) = 8960x - 2600. Interpret slope in context.Group of answer choicesFor every additional carat in weight of a diamond, the price goes down $8960.For every additional carat in weight of a diamond, the price goes down by $2600.For every additional carat in weight of a diamond, the price goes up by $2600.For every additional carat in weight of a diamond, the price goes up $8960.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.