The price of a diamond is directly proportional to the square of its weight. A diamond is broken into three pieces whose weights are in the ratio 4 : 3 : 1, and selling the pieces causes a loss of Rs 5,700. What was the price of the diamond before it was broken?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 9,600
When price varies as the square of the weight, price \(=k\times(\text{weight})^{2}\). Breaking the piece keeps the total weight but lowers the total price, because the sum of the squares of the parts is smaller than the square of the whole.
Weights of the pieces: \(4w,\ 3w,\ w\); whole diamond \(8w\)
Price of the whole diamond \(=k(8w)^{2}=64kw^{2}\)
Price of the pieces \(=k(16+9+1)w^{2}=26kw^{2}\)
Loss \(=64kw^{2}-26kw^{2}=38kw^{2}=5700\), so \(kw^{2}=150\)
Price before breaking \(=64\times150=\) Rs 9,600
The diamond was worth Rs 9,600.