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
Question
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
Solution
Let's solve this step by step:
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The weight of the diamond was split into a ratio of 3:2:1, which adds up to 3+2+1 = 6 parts.
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The cost of the diamond is proportional to the square of its weight. So, the loss incurred due to breaking the diamond into three pieces would be the difference between the square of the original weight and the sum of the squares of the weights of the individual pieces.
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Let's assume the original weight of the diamond to be 6x (as the total parts is 6). Therefore, the cost of the original diamond would be (6x)^2.
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The diamond broke into pieces with weights 3x, 2x, and 1x. So, the total cost of the broken pieces would be (3x)^2 + (2x)^2 + (1x)^2.
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The loss incurred is the difference between the original cost and the cost of the broken pieces, which is given as Rs 46200.
So, we can set up the equation as follows:
(6x)^2 - [(3x)^2 + (2x)^2 + (1x)^2] = 46200
Solving this equation will give us the value of x, and substituting this value in the equation (6x)^2 will give us the initial cost of the diamond.
Let's solve it:
36x^2 - [9x^2 + 4x^2 + x^2] = 46200 36x^2 - 14x^2 = 46200 22x^2 = 46200 x^2 = 46200 / 22 x^2 = 2100 x = sqrt(2100) x = 45.83 (approx)
Substitute x in the equation (6x)^2 to get the initial cost of the diamond:
(6*45.83)^2 = Rs 75600 (approx)
So, the initial cost of the diamond was Rs 75600.
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