The logic here is that the sum of all place values of the letters is added to the sum of first and last letter of the word -

B (2) + O (15) + T (20) + T (20) + L (12) + E (5) = 74

74 + B (2) + E (5) = 81

P (16) + E (5) + R (18) + S (19) + O (15) + N (14) = 87

87 + P (16) + N (14) = 117

Similarly,

B (2) + A (1) + N (14) + A (1) + N (14) + A (1) = 33

33 + B (2) + A (1) = 36

Hence, option B is the correct answer.

• "About" means concerning which should be followed by a matter or topic and not a person. Hence, it is wrong.

• "For" shows a reason or a purpose and thus it is out of context.

• "Among" is used for for three or more persons or things and "between" is used for two persons or things.

• For example:
  
  I. Divide the mango between Ram and Ratna.
  
  II. Divide the mango among all the children.

• Here we can see the mention of "both the men" which indicates that there were "two men".

• Thus, "between" is the correct preposition to fill in the blank.

The phrasal verb “come across” means “meet or find by chance”. Here the sentence suggests a context of a weird train that the subject found. So there should be “across” in the blank.

Hence option C is correct.

“With” is used before the instrument with which a person does a thing. For example

He wrote the letter with a pencil.

Here in the sentence “rifle” is the instrument. So there should be “with” in the blank. Hence option B is correct.

• The phrasal verb “carry out” means “to do or complete something, especially that you have said you would do or that you have been told to do”.
  e.g. Our soldiers carried out a successful attack last night.
  
• Here the sentence suggests a context of wishes that the subject wants to complete.
  
• So there should be “out” in the blank. 

 The verb “abhorrence” takes the preposition “of”. So there should be “of” in the blank. Hence option B is correct.

“Besides” means “apart from” or “in addition to”.
For e.g. I have no other family besides my parents.

Here the sentence talks about the instruments other than those which the astronomers use.
Hence, option A is correct.

* The use of “gets into” suggests that the word “trouble” will fit in the blank.

* “Get into trouble” is a fixed phrase.

Hence, option C is the correct answer.

* The blank needs an adjective for the noun “shower”.

* The sentence tells us that the person “I” was running late.

* Thus, “quick” is the correct word for the blank.

Hence, option C is the correct answer.

Clouding = to make someone confused, or make something more difficult to understand

Shouting = (of a person) utter a loud cry, typically as an expression of a strong emotion.

Persuading = induce (someone) to do something through reasoning or argument.

Plotting = secretly make plans to carry out (an illegal or harmful action).

* The sentence talks about how negative and toxic thoughts make it difficult for us to think positively.

* Thus, “clouding” is the correct word for the blank.

Hence, option A is the correct answer.