Multiple choice

The cost of a precious stone varies directly as the cube of its weight. This stone is broken into three pieces with their weights in the ratio 2 : 3 : 5. If the loss in total value of the diamond was Rs. 94,080, what was the price of the original diamond?

  1. Rs. 1,12,000

  2. Rs. 17,920

  3. Rs. 11,200

  4. Rs. 1,12,500

  5. None of these
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A Correct answer
Explanation

Let weight be W. Value V = kW^3. Original value = k(2+3+5)^3 = 1000k. New value = k(2^3 + 3^3 + 5^3) = k(8 + 27 + 125) = 160k. Loss = 1000k - 160k = 840k. Given 840k = 94080, k = 112. Original price = 1000 * 112 = 112,000.

AI explanation

Using the direct cube variation method, if the original weight is 10x, the weights of the three broken pieces are 2x, 3x and 5x. The original value is proportional to (10x) cubed, which is 1000x squared, while the combined value of the pieces is proportional to (2x) cubed plus (3x) cubed plus (5x) cubed, totaling 160x cubed. The loss in value is 840x cubed, which equals 94080 rupees, meaning 1x cubed equals 112 rupees. Multiplying this unit value by the original 1000x cubed gives the original price of Rs. 1,12,000.

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