The cost of a diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio of 4 : 3 : 2 : 1 .When the pieces were sold, the merchant got ₹63,000 less than that of one piece. Find the original price of the diamond.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. ₹90,000.
The cost of a diamond varies directly from the square of its weight.
The ratio of the four pieces of diamonds = 4 : 3 : 2 : 1
Price ∝ (Weight)2
⇒ Price = k(Weight)2
Let the weights of the four pieces now be 4x, 3x, 2x, and x respectively.
New price = k(4x)2 + k(3x)2 + k(2x)2 + k(x)2 = 30kx2
Original price of unbroken diamond = k(4x + 3x + 2x + x)2 = 100kx2
So, 100kx2 - 30kx2 = 63000
⇒ 70kx2 = 63000
⇒ kx2 = 63000/70 = 900
⇒ 100kx2 = 900 × 100 = 90000
Therefore, the original price of the diamond is ₹90,000.