To understand the answer, let`s take a closer look at each option:

Option 1: 60°. In a clock, a full rotation (360°) is divided into 12 hours, that is 30° for each hour. Here, if the hour hand is at 3 and the minute hand is at 15 minutes (which is a quarter past), then they are one hour space apart which would be a 30° difference, not a 60° difference.

Option 2: 52 ½°. As explained in option 1, one hour space on a clock corresponds to a 30° angle. Thus, a 52 ½° angle would correspond to an interval slightly less than two hours, which is more than the time difference here.

Option 3: 47 ½°. The hour and minute hands at 3:15 are not exactly on the `3` and `15` mark. Remember, the hour hand also moves as minutes pass. When it`s 3:15, the hour-hand is quarter way between 3 and 4. So, the angle is bit less than 30° which is listed as 47 ½°.

Option 4: 42°. This is