Question

A diamond falls and breaks into pieces whose weights are in the ratio ` 2 : 3 : 5`. The value of the diamond is directly proportional to the square of its weight. Find the loss incurred, if the actual cost of the diamond is Rs. 96, 000 . (in Rs.)
A. ` 36, 480`
B. ` 59, 520`
C. ` 72,960`
D. None of these

Answer 1

Correct Answer - B
Let the weights of the three pieces be 2x, 3x and 5x and their costs be `v_(1), v_(2) and v_(3)` respectively.
`v_(1) = 4x^(2)k, v_(2) = 9x^(2)k, v_(3) = 25 x^(2)k`,
` 96,000 = 100x^(2)k`
` x^(2)k=960 `
`v_(1)+v_(2)+v_(3) = 38x^(2)k`
` = 38 xx 960 = 36, 480`,
`:." loss " = 96,000-36,480 = Rs. 59,520`.

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Thanks