Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2010 · Marks: · Difficulty:
Cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio 1 : 2 : 3 : 4. If the loss in the total value of the diamond was ` 70000, find the price of the original diamond.
Answer
Answer (as printed):
Explanation
Let the weights of the four pieces be $x, 2x, 3x$ and $4x$. Then, original weight of the diamond $=(x+2x+3x+4x)=10x$. Original price of the diamond $=k\times(10x)^2=100kx^2$, where $k$ is a constant. Prices of the smaller pieces will be $kx^2, 4kx^2, 9kx^2$ and $16kx^2$. Total price of the four pieces $=(kx^2+4kx^2+9kx^2+16kx^2)=30kx^2$. Loss in value $=(100kx^2-30kx^2)=70kx^2$. $$\therefore \quad 70kx^2=70000 \text{ or } kx^2=1000.$$ Hence, price of original diamond $=₹(100\times 1000)=₹100000$.
Explanation as extracted from the printed page; notation may be imperfect.