The correct option is
A is cooked
In the answer given by 'B' to 'A', a verb is missing. Thus, the answer must be a verb. Further, the doer of the action, that is, the one who cooks(the elder sister), is becoming the object from the subject. Thus, the answer is in the passive voice. 'cooks' in 'A' indicates that 'A' is in simple present tense. When the verb is in the simple present tense in the active voice, the verb in the passive voice is in the form of "finite form of the verb 'to be' in the same tense + past participle of the main verb".
Option A is correct. 'is cooked' is in the form of "finite form of the verb 'to be' in the same tense + past participle of the main verb". Thus, it is correct answer.
Option B is incorrect. In 'is cooking', although a finite form of the verb 'to be' is present, 'cooking' is the present participle form and not the past participle form of 'cook'. Thus, it is grammatically incorrect.
Option C is incorrect. 'has cooked' is in the present perfect tense, and the present perfect tense is not used in the passive voices of sentences unless the auxiliary has is followed by 'been'. Thus, it is grammatically incorrect
Option A is incorrect. In 'can cook', neither 'can' nor 'cook' is grammatically correct. This is because, 'can' is not a finite form of the verb 'to be' and 'cook' is also not the past participle form of the verb cook. Thus, it is incorrect.