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Broken Metal Beam Value

XAT 2025 · Quantitative Ability & Data Interpretation · Easy · Ratio and Proportion

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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?

  1. A.

    74.23% gain

  2. B.

    42.60% loss

  3. C.

    31.77% loss

  4. D.

    57.40% loss

  5. E.

    No gain or loss

Answer

B

Explanation

Let the lengths of the broken pieces be 4x4x and 9x9x. The original length was 13x13x. Market value is proportional to length2\text{length}^2. Original Value = k(13x)2=169kx2k(13x)^2 = 169kx^2. New Total Value = k(4x)2+k(9x)2=16kx2+81kx2=97kx2k(4x)^2 + k(9x)^2 = 16kx^2 + 81kx^2 = 97kx^2. Loss = 169kx2−97kx2=72kx2169kx^2 - 97kx^2 = 72kx^2. Percentage Loss = 72kx2169kx2×100=7200169%≈42.60%\frac{72kx^2}{169kx^2} \times 100 = \frac{7200}{169}\% \approx 42.60\% loss.

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