Q4
The market value of beams, made of a rare metal, has a unique property: the market value of any such beam is proportional to the square of its length. Due to an accident, one such beam got broken into two pieces having lengths in the ratio 4:9.
Considering each broken piece as a separate beam, how much gain or loss, with respect to the market value of the original beam before the accident, is incurred?
Answer: D
Asked: the percentage gain or loss when a beam whose value is proportional to (length)2 breaks in the ratio 4 : 9.
Take the pieces as \(4k\) and \(9k\), so the original beam was \(13k\). Value \(= c \times \text{length}^2\).
- Original value: \(169ck^2\)
- Pieces: \(16ck^2 + 81ck^2 = 97ck^2\)
- Loss: \(169 - 97 = 72\) parts
- Loss % \(= \frac{72}{169} \times 100 \approx 42.60\%\)
Answer: 42.60% loss