(a) The VILNA GA'ON explains that the reason why 22 years were added to Binyamin ha'Tzadik's life was because the Gemara earlier (9b) teaches that a person who appeases and encourages a poor person is blessed with 11 blessings. Binyamin ha'Tzadik appeased the poor woman and her seven sons when he said that he wished with all his heart that he could help her, but that the communal funds were depleted. He thereby appeased 8 people (the woman and her seven sons), and thus he was deserving of 88 blessings (11 X 8). The Chachamim teach (see Sotah 21a) that each blessing is comprised of three months of added life. 88 blessings times 3 months equals 264 months, or 22 years.

(b) The TORAS CHAIM writes that Binyamin ha'Tzadik was given an extra 22 years of life to correspond to the 22 letters with which the Torah was written, because he fulfilled the Torah's dictum, "Whoever saves one life is considered to have saved an entire world." (A similar reward of 22 years was granted to Rebbi Yosi, as the Zohar, Parshas Balak, relates.)

(c) The CHASAM SOFER explains that Binyamin ha'Tzadik was rewarded not only for the eight actual lives that he saved, but also for the lives of their descendants. This is based on the words of RASHI in Bereishis (4:10), who explains that Kayin was punished not only for killing his brother, but also for preventing the lives of his brother's descendants from coming into existence ("Kol Demei Achicha Tzo'akim"). Each of the woman's seven sons would bear, in the future, at least two children (a boy and a girl) in order to fulfill the Mitzvah of Piryah v'Rivyah. Hence, Binyamin ha'Tzadik saved the 8 lives of the woman and her seven sons, plus the 14 lives of the children of the seven sons. For these 22 lives, Binyamin ha'Tzadik was rewarded in this world with 22 extra years of life. (See also third explanation of BEN YEHOYADA.)

(See also MAHARSHA, BEN YEHOYADA, IYUN YAKOV, and EINAYIM LA'MISHPAT.)