NIMCET 2015 — Reasoning PYQ

The hands of a clock do not overlap every 60 minutes. Because the hour hand also moves, the minute hand actually takes about 65 minutes and 5 seconds to "catch up" and overlap with the hour hand again.

2. The Calculation:

• In a $12$-hour period, the hands overlap exactly $11$ times.

• The reason it is $11$ and not $12$ is because the overlap that would happen between $11:00$ and $1:00$ occurs exactly at 12:00. Thus, the $11$-to-$12$ and $12$-to-$1$ intervals share a single overlap point.

3. Total in 24 Hours:

Since the day consists of two $12$-hour cycles:

Summary of Clock hand movements in 24 hours:

• Overlapping (Coincide): 22 times

• Straight line (Opposite): 22 times

• Right angles (Perpendicular): 44 times

Correct Option: (b) 22