The price of gold is directly proportional to the square of its weight. A person broke a piece of gold into three pieces whose weights are in the ratio 3 : 4 : 5 and sold them, and he faced a loss of Rs 23,500. Find the price of the gold before it was broken.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 36,000
Price \(=k\times(\text{weight})^{2}\). Breaking the gold keeps the total weight, but the sum of the squares of the parts is less than the square of the whole; that drop is the loss.
Weights of the pieces: \(3w\), \(4w\) and \(5w\); whole piece \(=12w\)
Price of the whole piece \(=k(12w)^{2}=144kw^{2}\)
Price of the three pieces \(=k(9+16+25)w^{2}=50kw^{2}\)
Loss \(=144kw^{2}-50kw^{2}=94kw^{2}=23500\), so \(kw^{2}=250\)
Price before breaking \(=144\times250=\) Rs 36,000
The gold was worth Rs 36,000 before it was broken.