The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

  1. ₹ 1,00,000
  2. ₹ 1,40,000
  3. ₹ 1,50,000
  4. ₹ 1,75,000

Answer

Cost ∝ (weight)2

Total weight of original diamond = 1k + 2k + 3k + 4k = 10k, where k is positive integer

Cost of original diamond = (10k)2 = 100k2

Total cost of four broken pieces = k2(1 + 4 + 9 + 16) = 30k2

The value of broken pieces is 70,000 less than the original diamond.

Difference in cost = 70,000

100k2 - 30k2 = 70,000

70k2 = 70,000

k2 = 1,000

Cost of original diamond = 100k2 = 100 × 1,000

= 1,00,000

The correct option is A.

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