Xavier Aptitude Test 2025 Paper

Concept:The value of a beam is proportional to the square of its length, so value $= k \times (\text{length})^2$. Compare the total value of the two broken pieces with the value of the original whole beam.Explanation:Let the lengths of the two broken pieces be $4x$ and $9x$.Therefore, the length of the original beam before the accident is $4x + 9x = 13x$.Value of the original beam $= k(13x)^2 = 169kx^2$.Value of the first broken piece $= k(4x)^2 = 16kx^2$.Value of the second broken piece $= k(9x)^2 = 81kx^2$.So, total value of the two pieces after breakage $= 16kx^2 + 81kx^2 = 97kx^2$.Since $97kx^2 < 169kx^2$, there is a loss.Loss in value $= 169kx^2 - 97kx^2 = 72kx^2$.Loss percentage $= \frac{72kx^2}{169kx^2} \times 100 = 42.60\%$.Answer:There is a $42.60\%$ loss, so the correct option is B. $42.60\%$ loss.