Pariksha SaathiClock Questions with Solutions (Angle Between Hands)
Clock questions are a disguised speed problem — the hour and minute hands move at fixed rates, so finding the angle between them at any given time is just plugging into a formula. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- The minute hand completes 360° in 60 minutes, so it moves 6° every minute. The hour hand completes 360° in 12 hours (720 minutes), so it moves 0.5° every minute — it creeps forward steadily, not staying fixed at the hour mark.
- At M minutes past H o’clock: minute-hand angle (from 12) = 6 × M degrees. Hour-hand angle (from 12) = 30 × H + 0.5 × M degrees.
- Angle between the hands = the absolute difference between those two angles. If that difference is more than 180°, subtract it from 360° — "the angle between the hands" always means the smaller of the two possible angles.
- For "when are the hands opposite" (180° apart) or "when do they overlap" (0° apart) questions within a given hour, set up the equation using the formulas above and solve for M directly, rather than trying to picture it.
Worked examples
1. Find the angle between the hour and minute hands at 3:00.
Solution
- Hour-hand angle = 30 × 3 + 0.5 × 0 = 90°. Minute-hand angle = 6 × 0 = 0°.
- Difference = |90 − 0| = 90°.
Answer: 90°
2. Find the angle between the hour and minute hands at 4:30.
Solution
- Hour-hand angle = 30 × 4 + 0.5 × 30 = 120 + 15 = 135°. Minute-hand angle = 6 × 30 = 180°.
- Difference = |135 − 180| = 45°.
Answer: 45°
3. Find the angle between the hour and minute hands at 7:20.
Solution
- Hour-hand angle = 30 × 7 + 0.5 × 20 = 210 + 10 = 220°. Minute-hand angle = 6 × 20 = 120°.
- Difference = |220 − 120| = 100°.
Answer: 100°
4. At what time between 9 and 10 o’clock will the hour and minute hands be exactly opposite each other (180° apart)?
Solution
- Hour-hand angle at M minutes past 9 = 270 + 0.5M. Minute-hand angle = 6M.
- For the hands to be opposite: (270 + 0.5M) − 6M = 180 → 270 − 5.5M = 180 → 5.5M = 90 → M = 90/5.5 = 180/11 ≈ 16.36.
- So the hands are opposite at 9 hours and 180/11 minutes, i.e., 16 4/11 minutes past 9.
Answer: 9:16 4/11 (16 4/11 minutes past 9)
Try these yourself
Apply the formulas the same way, then check against the answer.
1. Find the angle between the hour and minute hands at 6:00.
Answer: 180°
2. Find the angle between the hour and minute hands at 2:40.
Answer: 160°
3. At what time between 2 and 3 o’clock will the hour and minute hands be exactly opposite each other (180° apart)?
Answer: 2:43 7/11 (43 7/11 minutes past 2)
Where this comes up
Clock is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.
Practice more Clock questions
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