How many times do the hour and minute hands of a clock coincide in a 24-hour period?

Appeared in: JIPMER Nursing Officer-2024

Explanation

The hands of a clock coincide when the minute hand overtakes the hour hand.
The minute hand moves faster than the hour hand. It takes the minute hand approximately 65.45 minutes (or 720/11 minutes) to lap the hour hand.
Because each 'lap' takes more than an hour, the hands only coincide 11 times in a 12-hour period.
Over a full 24-hour day, this occurs twice, so the total number of coincidences is 11 × 2 = 22.

Option A: This is the number of coincidences in a 12-hour period, not a 24-hour period.
Option C: This incorrectly assumes the hands coincide exactly once every hour. It fails to account for the continuous movement of the hour hand.
Option D: This is an arbitrary number, likely a guess based on the 12 hours marked on a clock face.

Visual 1: Animation - An animated clock face showing the movement of the hour and minute hands over a 12-hour period, with markers indicating each time they coincide. This helps visualize why the event doesn't happen exactly on the hour.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning - Clock Problems as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of problem tests logical reasoning and mathematical aptitude.
Strong reasoning skills are crucial for nurses in problem-solving, critical thinking, and making sound clinical judgments under pressure.
What if the question asked how many times the hands are perpendicular (at a 90-degree angle)? The hands are perpendicular 22 times in 12 hours, so they would be perpendicular 44 times in 24 hours.

How to Approach the Question

Identify the core of the question: It's about the relative speed of the clock hands.
Recall the movement: The minute hand moves 360° in 60 minutes. The hour hand moves 360° in 12 hours.
Understand the 'catch-up' concept: The hands start together at 12:00. For them to meet again, the minute hand must gain a full 360° on the hour hand.
Calculate for a 12-hour period first: Realize that because the 'catch-up' takes slightly more than an hour, one coincidence is 'lost' over the 12-hour cycle, resulting in 11 coincidences.
Extrapolate to the required 24-hour period: Double the result for 12 hours (11 x 2) to get the answer for 24 hours.

Concept Tested & Keywords

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Practise the full JIPMER Nursing Officer-2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.