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:
Question:
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:
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:
Options
Answer: 1296000
Explanation:
Step 1: Minimum total price Achieved when weights are close together: 3, 4, 5, 6 Total price = (3² + 4² + 5² + 6²) × k = (9 + 16 + 25 + 36)k = 86k Step 2: Maximum total price Achieved when weights are far apart: 1, 2, 3, 12 Total price = (1² + 2² + 3² + 12²) × k = (1 + 4 + 9 + 144)k = 158k Step 3: Find k Difference = 158k − 86k = 72k = 288,000 → k = 288,000 / 72 = 4,000 Step 4: Price of original stone Original price = 324k = 324 × 4,000 = 1,296,000 Answer: 1,296,000
Explanation:
Step 1: Minimum total price Achieved when weights are close together: 3, 4, 5, 6 Total price = (3² + 4² + 5² + 6²) × k = (9 + 16 + 25 + 36)k = 86k Step 2: Maximum total price Achieved when weights are far apart: 1, 2, 3, 12 Total price = (1² + 2² + 3² + 12²) × k = (1 + 4 + 9 + 144)k = 158k Step 3: Find k Difference = 158k − 86k = 72k = 288,000 → k = 288,000 / 72 = 4,000 Step 4: Price of original stone Original price = 324k = 324 × 4,000 = 1,296,000 Answer: 1,296,000
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