A diamond falls and breaks into three pieces whose weights are in the ration 1 : 3 : 6. The value of the diamond is proportional to the square of its weight. If the original value is Rs. 30,000. What is the loss in the value due to the breakage?
Question
A diamond falls and breaks into three pieces whose weights are in the ration 1 : 3 : 6. The value of the diamond is proportional to the square of its weight. If the original value is Rs. 30,000. What is the loss in the value due to the breakage?
Solution
Sure, let's solve this step by step.
Step 1: Understand the problem The diamond breaks into three pieces with weights in the ratio 1:3:6. The value of the diamond is proportional to the square of its weight. This means that if the weight of the diamond increases, its value increases by the square of the weight.
Step 2: Calculate the total weight ratio The total weight ratio of the diamond pieces is 1+3+6 = 10.
Step 3: Calculate the original value The original value of the diamond is Rs. 30,000. This is when the diamond is whole and not broken into pieces.
Step 4: Calculate the value of the broken pieces The value of the diamond pieces is proportional to the square of their weights. So, the value of the pieces are as follows:
- Piece 1: (1^2)/10 = 0.1 of the original value
- Piece 2: (3^2)/10 = 0.9 of the original value
- Piece 3: (6^2)/10 = 3.6 of the original value
Step 5: Calculate the total value
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