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} = 100k^{2}

Total cost of four broken pieces = k^{2}(1 + 4 + 9 + 16) = 30k^{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

**The correct option is A.**