Weight-length proportionality (uniform rod): A 13 m long rod weighs 23.4 kg. Assuming uniform density, what is the weight of a 6 m long rod of the same material and cross-section?

Introduction / Context:
For a uniform rod (same material and cross-section), weight is directly proportional to length. The unitary method gives the per-metre weight, which we then multiply by the required length. This is a standard proportionality application in aptitude and basic physics contexts.

Given Data / Assumptions:

• Length L1 = 13 m, Weight W1 = 23.4 kg
• Find weight W2 for length L2 = 6 m
• Uniform rod: weight ∝ length

Concept / Approach:
Compute weight per metre as W1 / L1, then multiply by L2. Because both numbers divide neatly, the final result is exact to one decimal place without complex rounding.

Step-by-Step Solution:

Verification / Alternative check:
Proportion check: W2/W1 = L2/L1 = 6/13. Thus W2 = 23.4 * (6/13) = 23.4 * 0.461538… = 10.8 kg (matches the direct unitary calculation).

Why Other Options Are Wrong:

• 7.2, 9.0: underestimate the proportional weight.
• 12.4, 18.0: overshoot the proportional weight for 6 m.

Common Pitfalls:
Dividing 23.4 by 6 instead of by 13, or mixing metres and kilograms. Always compute per-unit length correctly before scaling to the target length.

Final Answer:
10.8 kg