Step 1: Identify the construction being tested.
The sentence begins with "The reason why... is because...". This is the well-known "reason is because" error.
Step 2: Understand why it is wrong.
"Reason" and "because" both express cause, so using them together is redundant, since "because" essentially restates the idea already carried by "the reason". In formal English, "reason" should be followed by "that", not "because", to introduce the explanation as a noun clause acting as the complement of "reason".
Step 3: Apply the correction.
The sentence should read "The reason why she is absent today is that her husband is ill." This keeps the tense consistent (present tense "is" throughout, since both the absence and the illness are current) and replaces "because" with "that".
Step 4: Eliminate the other options.
Option (b) drops the linking verb "is" and breaks the sentence structure. Option (d) is grammatically broken ("her husband illness" is not a complete clause). Option (e) shifts everything to the past tense unnecessarily, changing the intended meaning. Option (a) repeats the original "reason is because" error.
Step 5: Conclusion.
Option (c), "Absent today is that her husband is ill", correctly completes the sentence.