Multiple choice

Price of a piece of diamond is Rs. 2000. It is broken into two equal pieces. If price of diamond is directly proportional to the square of its weight, then the amount of loss for breaking into two pieces is

  1. Rs. 500

  2. Rs. 1500

  3. Rs. 2000

  4. Rs. 1000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial price P = k * w^2 = 2000. Broken into two equal pieces, each weight is w/2. New price = k * (w/2)^2 + k * (w/2)^2 = k * (w^2/4 + w^2/4) = k * w^2 / 2. New price = 2000 / 2 = 1000. Loss = 2000 - 1000 = 1000.

AI explanation

Assuming the initial weight of the diamond is 2 units, the original price is based on the square of the weight, so it is proportional to 2 squared, resulting in a factor of 4. When broken into two equal pieces of 1 unit each, the total new price is proportional to 1 squared plus 1 squared, which equals 2. The price drops by half of its original value, making the loss equal to Rs. 1000.

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