The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is
Explanation:
Price (P) ∝ (weight)2 ⇒ P = k × w2
Total value after breaking of the stone will be highest if one of the pieces is as heavy as possible and others are as light as possible i.e., the weights of the pieces are 1, 2, 3 and 12 units. ∴ Total value in this case = k × (1)2 + k × (2)2 + k × (3)2 + k × (12)2 = 159k
Total value after breaking of the stone will be least if weights of the pieces are as close to each other as possible i.e., the weights of the pieces are 3, 4, 5, and 6 units. ∴ Total value in this case = k × (3)2 + k × (4)2 + k × (5)2 + k × (6)2 = 86k
⇒ 158k – 86k = 288000 ⇒ 72k = 288000 ⇒ k = 4000
∴ Weight of original stone = 4000 × (18)2 = 1296000.
Hence, option (b).
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