Clocks
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Quantitative Aptitude - Clocks
In-depth guide on angle- and error-related clock problems: angles, overlaps, gains/losses.
1. Hour‑Minute Hand Angle
Formula: \( |30H - 5.5M| \). E.g., at 2:20: |60 - 110| = 50°.
2. Hand Overlaps
- Every \( \frac{720}{11} \approx 65.4545 \) minutes past each hour.
- nᵗʰ overlap time = \( \frac{720n}{11} \) minutes after 12.
Example: 3rd overlap → 196.36 min → 3h 16m 22s.
3. Opposite Hands (straight 180°)
Equation: |30H - 5.5M| = 180 → Solve for M.
4. Clock Gain/Loss
Daily gain = d seconds/day → rate per minute = d/(24×60×60) sec/sec. Actual time vs indicated calculate via proportional error.
5. Sample Problems
- Angle at 9:15: |270 - 82.5| = 187.5° → minimal = 360-187.5 = 172.5°.
- Clock gains 6 min in 24h: After 10h, gain = 6×10/24 = 2.5 min → indicated and real times differ accordingly.
6. Exam Strategy
- Always convert angles to ≤180°.
- Use exact fraction (±1 min) for overlap times.
- For gain/loss, convert to per‑second rate first.
7. Common Errors
- Applying hour-hand position as 30H without adding 0.5 per minute.
- Ignoring minute-hand movement during gain/loss problems.
8. Quick Checklist
- Practice 7 angles, 5 overlaps, 5 gain/loss problems.
Summary: Angle formula + overlaps (720/11) + time‑error rates = fast solutions. Mind units and minimal angles.
Topics
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