Track condition quantification: If a is the number of peaks > 10 mm of unevenness per km, b is peaks > 6 mm of gauge variation per km, and c is peaks > 2 mm twist per metre, what is the Composite Current Recording Index (Ic) recommended by Northern Railway?

Introduction / Context:
Track-recording cars measure defects in longitudinal level (unevenness), gauge variation, and twist. A composite index condenses these readings into a single value for maintenance prioritization. The Northern Railway formula is a commonly cited benchmark in Indian practice.

Given Data / Assumptions:

• a = average peaks of unevenness > 10 mm per km.
• b = average peaks of gauge variation > 6 mm per km.
• c = average peaks of twist > 2 mm per metre.

Concept / Approach:
The composite index penalizes the Ic value for higher counts of defects. Unevenness and gauge peaks have full weight; twist is down-weighted (divided by 4) recognizing its different scaling/occurrence frequency.

Step-by-Step Solution:
Adopt the recommended form Ic = 30 - a - b - c/4.Interpretation: higher a, b, or c reduces Ic, signaling worse track condition.Plan maintenance when Ic drops below specified thresholds.

Verification / Alternative check:
Try sample values: if a = 10, b = 6, c = 8, then Ic = 30 - 10 - 6 - 2 = 12, indicating significant defects and need for attention.

Why Other Options Are Wrong:

• 10, 20, or 40 as the constant base do not match the Northern Railway guidance for the stated thresholds.
• 50 is not standard for this formulation.

Common Pitfalls:

• Mixing thresholds from different administrations or older manuals.
• Forgetting to divide twist peaks by 4.

Final Answer:
Ic = 30 - a - b - c/4.