Multiple choice

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 : 2 : 3 : 4. If the loss in total value of the diamond was Rs. 70,000, what was the price of the original diamond?

  1. Rs. 1,00,000

  2. Rs. 1,40,000

  3. Rs. 1,50,000

  4. Rs. 1,75,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let weights be x, 2x, 3x, 4x. Total weight = 10x. Original price = k(10x)^2 = 100kx^2. Value of pieces = k(x^2 + 4x^2 + 9x^2 + 16x^2) = 30kx^2. Loss = 70kx^2 = 70,000. So kx^2 = 1000. Original price = 100 * 1000 = 100,000.

AI explanation

Let the cost of a diamond be directly proportional to the square of its weight, meaning Cost equals k times weight squared. The weights of the four broken pieces are in the ratio 1 : 2 : 3 : 4, so the total value of the broken pieces is proportional to 1 squared plus 2 squared plus 3 squared plus 4 squared, which equals 1 plus 4 plus 9 plus 16, totaling 30. If the original weight was the sum of the parts (1 plus 2 plus 3 plus 4 = 10), its original value was proportional to 10 squared, which is 100. The loss in value is 100 minus 30 = 70 units; since this loss equals Rs. 70,000, one unit equals Rs. 1,000, making the original price 100 times Rs. 1,000, which is Rs. 1,00,000.

Keep practicing — related questions