Fill in the blanks with the most appropriate words. While he _____ to school his elder brother ___ from the Institute. His brother is a teacher now.

The correct answer is: While he went to school his elder brother graduated from the Institute. His brother is a teacher now.

The other options are incorrect because they do not make sense in the context of the sentence.

• Option A: had gone / graduated is incorrect because it implies that the elder brother graduated before the younger brother went to school. This is not possible, as the younger brother would have had to be born before the elder brother graduated.
• Option B: has been gone / will graduate is incorrect because it implies that the elder brother has been gone from school for a long time and will graduate in the future. This is not possible, as the elder brother is already a teacher.
• Option C: is going / has been graduating is incorrect because it implies that the elder brother is currently in the process of graduating from school. This is not possible, as the elder brother is already a teacher.

Therefore, the correct answer is: While he went to school his elder brother graduated from the Institute. His brother is a teacher now.