To answer this question, you need to use your logical reasoning and common sense. Let's go through each option to understand why it is correct or incorrect:

Option A) He wants some exercise - This option is incorrect because it does not explain why he can only travel half way up in the lift and why he does not have to walk when it's raining. If he wanted some exercise, he could choose to walk any day regardless of the weather or the lift.

Option B) He is short - This option is correct because it explains why he can only travel half way up in the lift and why he does not have to walk when it's raining. The man is so short that he cannot reach the buttons for the higher floors in the elevator. When he goes down, he can press the ground floor button which is at the bottom. When he goes up, he can only press the button for half way up which is within his reach. However, when it's raining, he has an umbrella with him which he can use to press the button for the top floor.

Option C) The elevator is having power problem during that particular time - This option is incorrect because it does not explain why he does not have to walk when it's raining. If the elevator had a power problem, it would affect all the floors and not just the higher ones. Also, it would be unlikely that the power problem would occur every day at the same time.

Option D) The building is very old. So during raining, he could not walk on the steps. - This option is incorrect because it does not explain why he can only travel half way up in the lift. If the building was very old and had unsafe steps, he would not be able to walk on them at all, regardless of the weather or the lift.

The correct answer is B. This option is correct because it explains why he can only travel half way up in the lift and why he does not have to walk when it's raining.