Question
A solid diamond falls and break into three pieces whose
weights are in the ratio of 4 : 3: 2. The value of each piece is directly proportional to the cube of their weights. Given that the value of solid diamond is Rs. 29,160. Find the loss due to the breakage?Solution
Ratio of each piece of diamond = 4x : 3x : 2x ∴ Solid diamond = 4x + 3x + 2x = 9x ∴ Cost of solid diamond = (9x)³ = 729x³ Cost of broken diamond = (4x)² + (3x)² + (2x)² = 99x² ∴ Loss = 729 x³- 99x³ = 630x³ …..(i) Given, 729x³ = 29,160 ∴x³ = 29160/729 = 40 ∴ Loss = 630 × 40 = Rs. 25,200
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