The cost of a piece of diamond varies with the square of its weight. A diamond of Rs.6,084 value is cut into 3 pieces whose weights are in the ratio 3 : 2 : 1. Find the loss involved in the cutting.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Rs.3,718
Given:
The cost of a piece of diamond varies with the square of its weight
Calculations:
Let the weight of pieces be 3x, 2x and x
Total weight = 3x + 2x + x = 6x
⇒ Cost ∝ weight2
⇒ 36x2 = 6084
⇒ Total weight of the pieces = 9x2 + 4x2 + x2 = 14x2
⇒ Required difference = 36x2 - 14x2 = 22x2
Required loss = (6084/36x2) × 22x2 = Rs 3718