I would like to ask how they are related and if one can be used instead of the other one
They can't be substituted for one another. This conversation might explain it for you.
Por qué means "Why?" Por qué estás tan callada? Why are you so quiet?
Porque [one word, no accent] means "because" - Estoy cansado porque llegué tarde a casa anoche ; I am tired because I came home late last night.
As John just said very correctly "¿por qué?" means "why?" and "porque" (one word, no accent) means "because". But you may be wondering about these other two. Have a look at this C1 lesson.
Difference between por que and porqué
I hope this helps understanding the different meanings and uses of these words.
Un saludo cordial
Lesson says por el que and I assume por los que are commonly used but marked wrong in the test question. Only por que was accepted.
Sometimes por que is a combination of the preposition por + relative pronoun que. In this case it is more common to use it with the article (por el que, por la que...), but it could also be omitted.
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