This is a challenging question because it relies heavily on idiom rather than grammar. When talking about situations like the results of government or police action, it's common to use the passive voice or past participle to suggest either that the action includes some element of coercion, and/or that no particular individual is responsible.
Examples of this in a judicial context:
Criminal suspects are often detained in a police holding cell up to 96 hours depending on the severity of the crime.
The child shall be remanded to the custody of her maternal grandfather for the duration of these proceedings.
The evidence was placed in a police lockup, where any authorized officer might have had access to it.
Idiomatically, the present continuous "lodging" is more frequently used for things like vacation getaways. In this context, using it would suggest a nice, short-term stay, almost as if Ms. Saraswathi would be enjoying her stay at the prison. Meanwhile the past participle "lodged" suggests instead she is stuck there, for some indefinite length of time.
So the correct answer is "B", if only by process of elimination:
The magistrate later remanded her in judicial custody till October 1. Police sources said Ms. Saraswathi would be lodged in the Salem Women's Prison.
To put it another way: For excursions, you get to choose where to lodge. If someone else lodges you somewhere, it's not likely to be as pleasant.
Side note: The use of the verb "lodge" here is distinctly BrE. AmE would not use "lodged" but instead "incarcerated" or "held" (if for a criminal offense), or "housed" (if for observation or protection).