Practice Questions
Lane C — Arrangements & puzzles
Study step 26 of 26
40 MCQs ready
Concept Explanation
Clock problems in placement LR (IndiaBIX / PrepInsta style) focus on the angle between hands, when hands coincide or are perpendicular, mirror time, and fast or slow watches. Use degree movement, not guesswork.
Hand movement
- Minute hand: 360° in 60 min → 6° per minute.
- Hour hand: 360° in 12 h → 0.5° per minute (30° per hour).
- Relative speed: 5.5° per minute — hands close at this rate.
Angle at H:M (12-hour clock)
Angle = |30H − 5.5M| (take the smaller angle if the result exceeds 180°). Example: at 3:00, |90 − 0| = 90°.
Common patterns
| Asked for | Approach |
|---|---|
| Coincidence between H and H+1 | Minute ≈ 60H/11 after H o'clock |
| Right angle after H:00 | Solve |30H − 5.5M| = 90 for M |
| Mirror time | (11 − H) : (60 − M) on a vertical mirror |
| Gain/loss per hour | Scale dial reading vs true time (ratio method) |
How to solve fast
- Draw 12 at top; mark hour hand position as 30H + 0.5M degrees.
- Mark minute hand at 6M degrees.
- For overlap times, use relative speed 5.5°/min or the 60H/11 shortcut.
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Q1 EasyWhat is the angle (in degrees) between the hour and minute hands at 3:00?ExplanationAt 3:00 the hands are perpendicular (90°).
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Q2 EasyWhat is the angle between the hands at 9:00?ExplanationSame as 3:00 — a right angle.
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Q3 EasyWhat is the angle between the hands at 12:00 (noon)?ExplanationBoth hands point to 12.
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Q4 EasyWhat is the angle between the hands at 6:00?ExplanationHands point opposite — a straight line (180°).
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Q5 EasyWhat is the angle at 6:30?ExplanationHour at 195°, minute at 180° → 15°.
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Q6 EasyWhat is the angle at 8:00?Explanation30×8 = 240° vs 0° → 120°.
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Q7 EasyWhat is the angle at 2:00?Explanation30×2 = 60° apart.
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Q8 EasyHow many times do the hands coincide in 12 hours?ExplanationHands overlap 11 times in 12 hours.
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Q9 EasyMirror image of 6:30 is?ExplanationMirror formula gives 5:30.
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Q10 EasyThe minute hand gains 5.5 degrees per minute on the hour hand. How far apart do the hands move in 20 minutes?Explanation5.5° × 20 = 110° relative movement.
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Q11 EasyHow many degrees does the minute hand turn in 25 minutes?Explanation6° × 25 = 150°.
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Q12 EasyHow many degrees does the hour hand turn in 30 minutes?Explanation0.5° × 30 = 15°.
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Q13 EasyAt 11:00, what is the angle between the hands?Explanation30×11 mod 360 = 330° from 12; smaller angle 30°.
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Q14 EasyAt 4:00, what is the angle?Explanation30×4 = 120°.
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Q15 MediumWhat is the angle at 3:15?Explanation|30×3 − 5.5×15| = 7.5°.
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Q16 MediumWhat is the angle at 3:30?ExplanationHour hand at 105°, minute at 180° → 75°.
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Q17 MediumWhat is the angle at 6:15?ExplanationHour at 97.5°, minute at 90° → 97.5°.
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Q18 MediumWhat is the angle at 4:20?Explanation|120 − 110| = 10°.
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Q19 MediumWhat is the angle at 1:30?ExplanationHour at 45°, minute at 180° → 135°.
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Q20 MediumWhat is the angle at 12:30?ExplanationSmaller angle between hands is 165°.
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Q21 MediumAt what time between 2 o'clock and 3 o'clock will the hands coincide?ExplanationCoincidence near 2 h + 120/11 min ≈ 2:11.
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Q22 MediumAt what time between 1 o'clock and 2 o'clock will the hands coincide?ExplanationAbout 1 h + 60/11 min ≈ 1:05.
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Q23 MediumAt what time between 3 o'clock and 4 o'clock will the hands coincide?ExplanationAbout 3 h + 180/11 min ≈ 3:16.
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Q24 MediumHow many times are the hands at right angles in 12 hours?ExplanationTwo right-angle events per hour gap → 22 in 12 hours.
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Q25 MediumIf the time is 2:30, what time is shown in a vertical mirror (standard mirror-clock rule)?ExplanationMirror time: (11 − hour) : (60 − minute) → 9:30.
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Q26 MediumMirror image of 3:15 is?Explanation(11 − 3) : (60 − 15) = 8:45.
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Q27 MediumMirror image of 8:25 is?Explanation(11 − 8) : (60 − 25) = 3:35.
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Q28 MediumHow many minutes after 12 o'clock do the hands first coincide again?Explanation360 ÷ 5.5 ≈ 65.45 min.
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Q29 MediumA clock gains 5 minutes per hour. It is set correctly at noon. When it reads 1:00, what is the actual time?Explanation65 dial minutes = 60 true minutes → 60 dial min ≈ 55.4 true min.
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Q30 MediumAt 5:15, what is the angle between the hands?Explanation|150 − 82.5| = 67.5°.
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Q31 MediumAt 10:15, what is the angle?Explanation|300 − 157.5| = 142.5°.
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Q32 MediumAt 7:20, what is the angle?Explanation|210 − 120| = 100°.
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Q33 MediumAt what time between 7 and 8 do the hands coincide?ExplanationAbout 7 h + 420/11 min ≈ 7:38.
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Q34 MediumAt 9:30, what is the angle?ExplanationHour at 285°, minute at 180° → 105°.
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Q35 MediumHow many times in a day (24 hours) do the hour and minute hands form a straight line (0° or 180°)?Explanation11 coincidences + 11 oppositions per 12 hours → 44 in 24 hours.
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Q36 HardAt what time between 4 o'clock and 5 o'clock are the hands at right angles (first time after 4:00)?ExplanationFirst solution near 4 h + 60/11 min ≈ 4:05.
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Q37 HardA clock is set right at 12 noon. It gains 6 minutes for every 60 minutes of correct time. When the clock shows 3:36, what is the correct time?ExplanationShown minutes = (66/60) × true minutes; 216 shown → about 196 true min (3:16).
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Q38 HardA clock set at noon loses 4 minutes every hour. When the watch shows 4:48, what is the correct time?ExplanationWatch runs at 56/60 of true time; 288 shown min → about 309 true min (≈ 5:09, nearest 5:08).
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Q39 HardBetween 5 and 6, when are the hands at right angles for the first time after 5:00?ExplanationSolve 150 − 5.5M = 90 → M ≈ 10.9 min → about 5:11.
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Q40 HardA clock shows the correct time at 3 pm. It gains 3 minutes per hour. What is the correct time when it shows 9 pm?Explanation6 shown hours at 63/60 rate → 6×60×60/63 ≈ 343 min ≈ 5 h 43 min after 3 pm → about 8:43 pm (nearest 8:40).