Ravi left his home at 12 PM to reach his school. When he reached the school, the hour and minute hands of the clock were making an angle of 165 degrees.How much time did he take (approximately) to reach the school if he took less than an hour to reach the school?

To solve this problem, we need to understand how the clock hands move. In one hour, the minute hand makes a full circle of 360 degrees, while the hour hand moves 30 degrees (360 degrees / 12 hours).

At 12 PM, both the hour and minute hands are at 12, so they start from the same position.

The problem states that when Ravi reached school, the hour and minute hands were making an angle of 165 degrees. This means that the minute hand has moved 165 degrees ahead of the hour hand.

Since the minute hand moves 330 degrees more than the hour hand in one hour (360 degrees - 30 degrees), we can set up the following equation to find out how much time has passed:

165 degrees = x * 330 degrees

Solving for x gives us x = 165 / 330 = 0.5

So, Ravi took approximately 0.5 hours, or 30 minutes, to reach school.