The __________ of the two brothers is more hardworking.

The correct answer is elder. Both "elder" and "older" are comparative forms of the adjective "old," but they are used in slightly different contexts. Elder is primarily used when referring to siblings or family members, specifically to denote seniority in age within the family. It often carries a connotation of respect or established birth order and is typically used attributively before a noun, such as "my elder brother" or "the elder sister." Older, on the other hand, is a more general comparative form that can be used for people or things to indicate greater age. It can be followed by "than" (e.g., "He is older than me") or used attributively (e.g., "the older car"). Since the question specifically refers to "the two brothers," "elder" is the more idiomatic and appropriate choice for comparing age within a family context. Old is the base adjective, and oldest is the superlative form, used when comparing three or more individuals or items.