The price of a piece of gold is directly proportional to the square of its weight. A piece of gold is broken into three pieces whose weights are in the ratio 3 : 2 : 1, and selling the pieces causes a loss of Rs 4620. What was the price of the piece before it was broken?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 7560
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: \(3w,\ 2w,\ w\); whole piece \(6w\)
Price of the whole piece \(=k(6w)^{2}=36kw^{2}\)
Price of the pieces \(=k(9+4+1)w^{2}=14kw^{2}\)
Loss \(=36kw^{2}-14kw^{2}=22kw^{2}=4620\), so \(kw^{2}=210\)
Price before breaking \(=36\times210=\) Rs 7560
The piece was worth Rs 7560.