To understand why the correct answer is option 'B', let's first discuss the concept of deflection in a simply supported beam.

Deflection in a beam refers to the vertical displacement or deformation that occurs when a load is applied to the beam. It is an important factor to consider in structural engineering as excessive deflection can lead to structural failure or discomfort for occupants.

The deflection of a simply supported beam depends on several factors, including the span of the beam and its effective depth. The effective depth of a beam is the distance from the centroid of the beam cross-section to the extreme fiber, where the maximum stress occurs.

Now, let's analyze the given options:

a) 7: If the ratio of span to effective depth is limited to 7, it means that the beam is relatively shallow compared to its span. This restriction on the ratio is quite conservative and may not be practical in many design scenarios. Therefore, option 'a' is unlikely to be the correct answer.

b) 20: This option suggests that the ratio of span to effective depth should not exceed 20. This is a more reasonable and commonly used limit in structural design. It allows for a greater range of beam depths while still ensuring that deflection remains within acceptable limits. Hence, option 'b' is a plausible answer.

c) 26: If the ratio of span to effective depth is limited to 26, it means that the beam can have a relatively larger depth compared to its span. This restriction may result in deeper beams, which might not be necessary for all design scenarios. Therefore, option 'c' is less likely to be the correct answer.

d) 13 mm: This option suggests that the maximum allowable deflection of the beam should not exceed 13 mm. However, the question is asking about the ratio of span to effective depth, not the actual deflection limit. Therefore, option 'd' is not the correct answer.

In conclusion, the correct answer is option 'B' (20), as it provides a reasonable limit on the ratio of span to effective depth while ensuring that the deflection of the simply supported beam remains within permissible limits.