Option B: 'Exhausted' means 'drained of strength or energy'. It relates to the given sentence: the person was drained of energy due to working.
Hence option B is correct.
Option A: 'Burnt' means 'to be on fire' or 'come in contact with something very hot and get injured'.
Option C: 'Faint' means 'feeling weak or dizzy'. We use this word when the person is in a state of losing consciousness.
Option D: 'Vexed' means 'irritated or annoyed'.
These words do not complete the sentence in meaning, and 'exhausted' is the most appropriate option.
Hence options A, C and D are incorrect.