The cost of a diamond varies directly as the square of its weight
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?
- ₹ 1,00,000
- ₹ 1,40,000
- ₹ 1,50,000
- ₹ 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.