Clock Notes
Clock logical reasoning ek aisa topic hai jahan pe practice aur concept dono zaruri hote hain. Government exams like SBI PO, SSC CGL, CAT etc. me ye topic aata hai aur agar aap tricks se maahir ho jayein, to ek minute me multiple questions solve kar sakte hain. Iss article me hum discuss karenge:
1. Angle Between Hands
Sabse pehle samjhte hain ki clock ke hour aur minute hands ke beech angle kaise nikaalte hain. 12 ghante ka dial 360° cover karta hai, to har ghanta = 30°. Minute hand ek minute me 6° (360/60) move karta hai, aur hour hand ek minute me 0.5° (30/60) move karta hai. Angle = |30H - (11/2)M|.
2. 60 Minutes = 360 Degrees Concept
Yahan trick ye hai ki 1 minute = 6°, to agar aapko kisi given time pe minute hand ka position jaana ho, minutes se 6 multiply kar do. For example, 15 minutes pe 15×6 = 90°.
3. Relative Speed Method
Hour aur minute hand ki relative speed difference hai: 6° - 0.5° = 5.5° per minute. Ye speed use karke hum wo moments find kar sakte hain jab dono hands overlap karte hain ya 180° apart hote hain. Formula: t = (H×30) / 5.5 minute.
4. Important Shortcuts
Overlap: Hands overlap approx. every 65 minutes aur total 11 baar 12 ghante me.
Straight Line: 180° alignment ke liye t = (H×30 + 180)/5.5.
Other Fast Trick: 4:43 pe overlap hota hai kyunki 4×30 + (M−65)×0.5 = 6M.
5. Clock Faces aur Types
Different clock faces hote hain: analog, digital, 24-hour clock. Analog clock questions me angle aur speed trick sabse important hai. Digital clocks me time format convert karke solve karte hain.
6. Sample Practice Questions
Q1. 3:15 pe hands ke beech angle kitna hoga?
Solution: Angle = |30×3 - (11/2)×15| = |90 - 82.5| = 7.5°.
Q2. Kab hour aur minute hand 90° form karte hain between 4 aur 5?
Solution: Solve |30H - (11/2)M| = 90. Put H=4, solve M => approx 38.18 minutes.
7. Tips & Tricks
1) Hammesha absolute value use karo angle formula me.
2) Practice ke liye daily 5-10 questions roz do.
3) Overlap aur 180° ke short forms yaad rakho.
4) Jaldi calculate karne ke liye mental math improve karo.
8. Familiar Examples
- Movie start time: Agar movie 3:20 par start ho aur aapko minimum angle dekhna ho, to trick use karo math speed.
- Train departure: 6:45 pe kitne angle honge? Ye real life time management me bhi help karta hai.
9. Practice Set Download
Neeche diye gaye button pe click karke aap pura detailed PDF notes download kar sakte hain, jisme aur bhi examples aur practice questions hain.
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