A stone worth Rs. 3000 drops and breaks with weight in

Solution

The stone breaks into pieces whose weights are in the ratio 1 : 2 : 3 : 4. Let the weights of the four pieces be: x, 2x, 3x and 4x So, total weight of the original stone = x + 2x + 3x + 4x = 10x Given, price of the stone is proportional to the square of its weight. So, value of original stone ∝ (10x)² = 100x² Also, original value of stone = Rs. 3000 Now, total value of broken pieces ∝ x² + (2x)² + (3x)² + (4x)² = x² + 4x² + 9x² + 16x² = 30x² Therefore, Value of broken pieces = (30x²/100x²) × 3000 = (30/100) × 3000 = Rs. 900 So, total loss = Original value - Value after breaking = 3000 - 900 = Rs. 2100 Hence, the total loss is Rs. 2100.