Question

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?

Accepted Answer

B. Let the lengths of the broken pieces be $4x$ and $9x$. The original length was $13x$. Market value is proportional to $	ext{length}^2$. Original Value = $k(13x)^2 = 169kx^2$. New Total Value = $k(4x)^2 + k(9x)^2 = 16kx^2 + 81kx^2 = 97kx^2$. Loss = $169kx^2 - 97kx^2 = 72kx^2$. Percentage Loss = $\frac{72kx^2}{169kx^2} 	imes 100 = \frac{7200}{169}\% \approx 42.60\%$ loss.

Broken Metal Beam Value

Explanation

Practise this under exam conditions