This is a question of degree of comparison of adjectives. Adjectives are used to describe, identify, modify or quantify nouns or pronouns. Adjectives have three degrees that compare one thing to another. The three degrees of adjectives are positive, comparative and superlative. The comparative and superlative degrees are used to compare between two and more than two subjects or objects respectively. In this question, the comparison is between two brothers so it should be a comparative degree.
Option A: It can be the correct answer as "elder" is in the comparative form. When referring to someone who is older than you in your family or someone who has a close relationship with you, you should use "elder". In this case, it is between two brothers so "elder" is the correct option.
Option B: "Oldest" is in superlative form. Secondly, in this case, a relationship is brought which signifies the use of elder. So this is the wrong choice.
Option C: Firstly, it is in the positive form and with that old cannot be used in this case.
Option D: It is in the superlative form (wrong choice)
Option A is the correct answer.