A precious stone weighing 70 grams worth 24,500 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred.
Explanation:
P = K × W2
⇒ 24,500 = K × 702 ⇒ K = 5.
Thus, our price and weight relationship is : P = 5W2.
When the two pieces are in the ratio 2 : 5 (weight wise) then we know that their weights must be 20 grams and 50 grams respectively. Their values would be:
10 gram piece : 5 × 202 = 2000;
25 gram piece : 5 × 502 = 12,500.
Total Price = 2,000 + 12,500 = 14,500. From an initial value of 24,500, this represents a loss of 10,000.
Hence, option (d).
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