At which of these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\circ$$? 
Overseas Competition->Knowledge Point->Word Problem Modules
At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\circ$$, the hour hand has turned $$\frac{150}{360}= \frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\circ$$ but, of these, only at $$7\text{pm}$$ does the minute hand point to $$12$$ and $$7\text{pm}$$ is not one of the times given.) 