The correct answer is A. 0.35 d.
The depth of the neutral axis is the distance from the top of the beam to the neutral axis, where the tensile and compressive stresses are equal. The depth of the neutral axis can be calculated using the following formula:
$d_n = \frac{0.577b}{f_y}$
where:
- $d_n$ is the depth of the neutral axis
- $b$ is the width of the beam
- $f_y$ is the yield stress of the steel
For a singly reinforced rectangular balanced section, the permissible stress in steel in tension is 140 N/mm2. Substituting this value into the formula, we get:
$d_n = \frac{0.577b}{140}$
$d_n = 0.35d$
Therefore, the depth of the neutral axis for a singly reinforced rectangular balanced section is 0.35 d.
Option B is incorrect because the depth of the neutral axis is not equal to 0.40 d. Option C is incorrect because the depth of the neutral axis is not equal to 0.45 d. Option D is incorrect because the depth of the neutral axis is not dependent on the grade of concrete.