Correct Answer - Option 1 : 1 in 333

__Concept:__

**Grade compensation:**

The ruling gradient is the maximum gradient on a particular section, but if a curve lies on a ruling gradient, the resistance due to gradient is increased by that due to curvature, and this further increases the resistance beyond the ruling gradient. In order **to avoid resistances beyond the allowable limits**, the gradients are reduced on curves, and this reduction is known as the grade compensation for the curve.

Allowable ruling gradient = Ruling gradient - Grade compensation

Grade compensation (GC) for **BG** = 0.04% per degree of curve

Grade compensation (GC) for **MG** = 0.03% per degree of curve

Grade compensation (GC) for **NG** = 0.02% per degree of curve

__Calculation__

Given,

Degree of curve D = 5°

Ruling Gradient = 1 in 200

So for 5° curve, compensation,

= 0.04 × 5 = 0.20%

∴ Ruling gradient \(= \frac{1}{{200}} \times 100 = 0.5{\rm{\% }}\)

∴ Allowable gradient = (0.5 - 0.2)% =\( {\rm{\;}}\frac{{0.3}}{{100}} = \frac{1}{{333}}\)

∴ Allowable Gradient = 1/333