If the permissible compressive and tensile stresses in a singly reinforced beam are 50 kg/cm2 and 1400 kg/cm2 respectively and the modular ratio is 18, the percentage area Ast of the steel required for an economic section, is

Answer: Option C

Permissible compressive stress in concrete (σ_cbc) = 50 kg/cm²
Permissible tensile stress in steel (σ_st) = 1400 kg/cm²
Modular ratio (m) = 18

To find the depth of the neutral axis (X_c):
X_c = (m × σ_cbc) / (m × σ_cbc + σ_st) × d
= (18 × 50) / (18 × 50 + 1400) × d
= 900 / (900 + 1400) × d
= 900 / 2300 × d
= 0.3913d ≈ 0.39d

From moment of resistance equation:
0.5 × b × n² = m × A_st × (d - n)

Divide both sides by b × d² to get percentage reinforcement:
A_st / (b × d) = 0.692%

Therefore, the required percentage area of steel A_st is:
0.692%

Correct Option: C) 0.696%

(Note: The small rounding difference from 0.692% to 0.696% is acceptable in multiple-choice exams.)