Question

Which of the following statements would you consider to be TRUE about the hour and minute hands of analogue clocks?

• A. The hour hand and the minute hand would make 90 degrees angle with each other 24 times in a day
• B. The hour hand and minute hand will overlap less than 24 times in a day
• C. The hour hand and minute hand will overlap exactly on the hour number marker only once every half a day
• D. The hour hand and minute hand will make acute angle to each other for almost as long as it will make obtuse angle to each other during the entire day

Answer 1

The Correct Option is B, C, D

To determine the truth of the given statements about the hour and minute hands of analogue clocks, we need to analyze the relationships and patterns in their movements.

1. Overlap Occurrences: The hour and minute hands overlap approximately every 65.45 minutes, which means there are 22 overlaps in a 24-hour period. This supports the correctness of: "The hour hand and minute hand will overlap less than 24 times in a day."

2. Overlap on Hour Markers: Overlaps on exact hour markers (like 12:00, 1:00, etc.) occur once every 12 hours, as the hands align at 12:00. Hence, the statement "only once every half a day" is true.

3. Angles between Hands: Considering the angles, the hour and minute hands make both acute (less than 90 degrees) and obtuse (more than 90 degrees) angles as they move. Since they almost equally share the clock positions during a full rotation, we can say: "The hour hand and minute hand will make acute angle to each other for almost as long as it will make obtuse angle to each other during the entire day."

4. 90 Degrees Angle: The statement that they make a 90-degree angle 24 times isn't true, as this event occurs 44 times in a day (22 acute, 22 obtuse).

Statement	Truth
The hour hand and minute hand would make 90 degrees angle with each other 24 times in a day	False
The hour hand and minute hand will overlap less than 24 times in a day	True
The hour hand and minute hand will overlap exactly on the hour number marker only once every half a day	True
The hour hand and minute hand will make acute angle to each other for almost as long as it will make obtuse angle to each other during the entire day	True