The exemption of those who are weak due to illness or advanced age from offering the Obligatory Prayers and from fasting is explained in Questions and Answers. Bahá'u'lláh indicates that in "time of ill-health it is not permissible to observe these obligations" (Q and A 93). He defines old age, in this context, as being from seventy (Q and A 74). In answer to a question, Shoghi Effendi has clarified that people who attain the age of seventy are exempt, whether or not they are weak.
Exemption from fasting is also granted to the other specific categories of people listed in the Synopsis and Codification, section IV.B.5. See notes 20, 30 and 31 for additional discussion.