Correct Answer  Option 2 : Steepest gradient for the BG line = 0.42% and for the MG line = 0.44%
Concept:
The ruling gradient:
 It 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.
Grade compensation for different types of gauge is given in the below table:
Type of gauge

Grade Compensation

B.G

0.04% per degree of curve

M.G

0.03% per degree of curve

N.G

0.02% per degree of curve

Calculation:
Given
Ruling gradient = 1 in 200 = \({1 \over 200} \times 100\) = 0.5 %
Degree of curve = 2°
Case  I: For Broad Gauge(BG)
Grande compensation = 0.04% per degree of curve = 0.04 \(\times\) 2 = 0.08%
Now,
Grade provided = Ruling gradient – grande compensation
Grade provided = 0.5 – 0.08 = 0.42%
Case  II: For Meter Gauge(MG)
Grande compensation = 0.03% per degree of curve = 0.03 \(\times\) 2 = 0.06%
Now,
Grade provided = Ruling gradient – grande compensation
Grade provided = 0.5 – 0.06 = 0.44%
Hence, Steepest gradient for the BG line = 0.42% and for the MG line = 0.44%.