Rahul gives a crystal diamond ring to his wife Vijeta on their wedding anniversary However the ring ...........

Quant (SSC) Ratio, Proportion

Rahul gives a crystal diamond ring to his wife Vijeta on their wedding anniversary. However, the ring falls off Vijeta's hand and breaks into three pieces the weights of which are in the ratio of 2 : 3 : 4. The value of each piece is directly proportional to the square of their weights. The given value of the diamond in the ring was Rs. 24300. Find the loss due to breakage.

Rs. 14300

Rs. 11400

Rs. 14600

Rs. 15600

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Explanation:

Ratio of each piece of diamond = 2x : 3x : 4x
∴ Solid crystal diamond = 2x + 3x + 4x = 9x
∴ Cost of solid crystal diamond = (9x)² = 81x²
Cost of broken pieces of diamond = (2x)² + (3x)² + (4x)² = 29x²
∴ Loss = 81x² – 29x² = 52x²
Given, 81x² = 24300
∴ x² = 24300 /81 = 300
∴ Loss = 52 × 300 = Rs. 15600.