The cost of a diamond varies directly as the square of its weight A diamond broke into four pieces w...........

Quantitative Aptitude (CDS) Ratio, Proportion

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 Rs. 70,000, what was the price of the original diamond?

Rs.1,00,000

Rs. 1,40,000

Rs.1,50,000

Rs. 1,75,000

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Explanation:

Ratio of weights of broken diamond = 1: 2: 3: 4
Net weight = x + 2x + 3x+ 4x= 10x
Price = 100 x²
Price = x² + 4x² + 9x² + 16x²= 30x²
Net loss = 100x²− 30x² = 70x²
Now,
70x² = 70000
=> x² = 1000
Price of original diamond = 100x²
= 100 × 1000
= 100000