Clocks Reasoning: Concepts, Tricks for RRB, SSC & Banking

Clocks Reasoning: Concepts, Formulas, Tricks

Target: RRB • SSC • Railway • Banking exam | Format: Concept notes + formula sheet + tricks + 10 multiple-choice questions (interactive answers)

This post gives concise, exam-focused notes on clocks reasoning — from basics to quick tricks — plus 10 fresh, exam-style MCQs with a Show Answer button for each. Use these to practice speed and accuracy for competitive exams.

1. Introduction to Clocks Reasoning

Clock problems test your ability to calculate angles between hour and minute hands, positions after a time, and relative motions. Most competitive-exam questions use an analog clock (12-hour dial). Understand the core rates and formulas below — they solve most problems quickly.

2. Basic Concepts & Important Rates

Minute hand speed: 360° in 60 minutes ⇒ 6° per minute.
Hour hand speed: 360° in 12 hours ⇒ 30° per hour ⇒ 0.5° per minute.
Relative speed between hands: 5.5° per minute (6 − 0.5) — used to find times between alignments.
Position formula: Angle of hour hand at H hours M minutes = 30×H + 0.5×M degrees.
Angle of minute hand: 6×M degrees.

Key formula (angle between hands):

Angle = |(30×H − 5.5×M)| or equivalently |(30H + 0.5M) − 6M|. If angle > 180°, take 360° − angle for the smaller angle.

3. Types of Clock Problems

Angle between hands at a given time (e.g., 3:15).
Time when hands are at a given angle.
Time between two successive events (e.g., when hands overlap next).
Relative motion problems (how long to gain/lose a certain angle).
Problems involving broken or stopped clocks, or clocks running fast/slow.

4. Short Tricks & Time-Saving Methods

Minute-hand shortcut: For minute M, minute-hand angle = 6M. So at 15 min → 90°.
Hour-hand micro-move: At H:M, hour-hand has moved M×0.5° beyond H×30°.
Overlap timings: Hands overlap roughly every 65⁄11 minutes (~5.4545 min after each hour). More exactly, overlaps occur at times given by T = (60/11)×H minutes after 12, but best memorized via formula when needed.
Opposite hands: Hands are opposite (180° apart) every 65⁄11 minutes too, offset by 30 minutes from overlap times.
When stuck: Compute both absolute angles and take the smaller of the two (angle and 360 − angle).

5. Solved Examples (quick)

Example 1: What is the angle between the hands at 3:15?

Hour angle = 30×3 + 0.5×15 = 90 + 7.5 = 97.5°. Minute angle = 6×15 = 90°. Angle = |97.5 − 90| = 7.5°. (Always pick the smaller angle.)

Example 2: When are the hands overlapping between 2 and 3 o’clock?

Overlap time after 2 = (60/11)×2 = 120/11 = 10 + 10/11 minutes ≈ 10:10 + 10/11 min ⇒ ≈ 2:10:54.5. So answer ≈ 2:10:54.5.

6. FAQs (Short)

Q: Which angle do we usually report — smaller or larger?: A: For most competitive exam problems, report the smaller angle between the hands (≤180°) unless the question explicitly asks for the larger angle.
Q: How to remember overlap times quickly?: A: Overlaps happen approximately every 65⁄11 minutes (~5.4545 minutes) after each overlap. Use formula Time = (60/11) × H minutes after 12 for the Hth overlap (or derive directly for a given hour).
Q: How many times do hands coincide in 12 hours?: A: 11 times (not 12). They coincide every 12/11 hours (~65.4545 minutes).

7. Quick Revision Checklist

Remember minute-hand = 6°/min, hour-hand = 0.5°/min.
Use angle formula: |30H − 5.5M| or compute absolute angles then difference.
Always choose the smaller angle (≤180°) unless asked otherwise.
Practice with fractional minutes (e.g., 27 3/11) — they appear often in overlap/opposite questions.