He has ............ a lot of money for his old age

The phrase “put aside” means to save something, like money, for future use. Therefore, Option B is the correct answer

The other options do not fit in this context. 

Option A: “Put off” means to delay or postpone something. 

Option C: “Put across” means to communicate or make something understood.

Option D: “Put through” typically means to connect a phone call or to make someone undergo a difficult situation. Therefore, “put aside” is the most appropriate choice here.