At 9 : 38 A.M. through how many degrees the hour hand of a clock moved since noon the previous day ?

Time from 12 noon to 9 : 38 A.M.
= 12 hours + 9 hours 38 minutes
= 21 hours 38 minutes
$$\eqalign{ & {\text{ = 21}}\frac{{38}}{{60}}{\text{ hours}} \cr & {\text{ = 21}}\frac{{19}}{{30}}{\text{ hours}} \cr & {\text{ = }}\frac{{649}}{{30}}{\text{hours}} \cr} $$
Angle traced by the hour hand in 12 hours = 360°
Angle traced by the minute hand in
$$\eqalign{ & \Leftrightarrow \frac{{649}}{{30}}{\text{hours}} \cr & = {\left( {\frac{{360}}{{12}} \times \frac{{649}}{{30}}} \right)^ \circ } \cr & = {649^ \circ } \cr} $$