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?
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?
A₹ 1,00,000
B₹ 1,40,000
C₹ 1,50,000
D₹ 1,75,000
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Correct answer is: ₹ 1,00,000
Explanation:
\(Cost ∝ (weight)^2\)
Total weight of original diamond = 1k + 2k + 3k + 4k = 10k, where k is positive integer
Cost of original diamond = \((10k)^2\) = \(100k^2\)
Total cost of four broken pieces = \(k^2\)(1 + 4 + 9 + 16) = 30\(k^2\)
The value of broken pieces is 70,000 less than the original diamond.
Difference in cost = 70,000
\(100k^2 - 30k^2 = 70,000\)
\(70k^2 = 70,000\)
\(k^2 = 1,000\)
Cost of original diamond = \(100k^2 = 100 × 1,000\)
= 1,00,000
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