Clocks · noteswale

1. Ye topic hai kya?

Do sui: hour (chhoti) aur minute (lambi). Sawaal: unke beech kitna angle, kab chipakengi, kab 90°, mirror mein kya time, ghadi tez/sust to asli time kya.

Shapes se farq

Wahan figure ulti. Yahan time aur degrees. Mirror yahan numbers palat-te hain (3:20 → 8:40), picture nahi.

Yahan kya nahi

Din-taarikh, leap year, odd days — calendar alag. Age problems alag. Yahan sirf analog clock.

2. Circle = 360°

12 hours = poora chakka = 360°.
1 hour mark (12→1) = 360/12 = 30°.
1 minute mark = 360/60 = 6°.
Minute hand: har minute 6°.
Hour hand: har minute 0.5° (kyunki 30° / 60 min = 0.5). Har hour 30°.

3:00

Hour 3 pe (90°), minute 12 pe (0°). Angle 90°.

6:00

Seedha saamne. 180°.

Galati: 3:20 pe hour hand ko 3 pe hi chhod dena. 20 minutes mein hour 20×0.5 = 10° aage khisak chuka hota hai.

3. Beech ka angle

H = hour (1 se 12, 12 ko 0 bhi le sakte). M = minutes (0–59).

Minute hand = 6M° (12 se clockwise).
Hour hand = 30H + 0.5M°.
Farq θ = |30H − 5.5M| (kyunki 30H + 0.5M − 6M = 30H − 5.5M).
Paper aksar chhota angle maangta: agar θ > 180, to 360 − θ lo.
Minute-spaces: 1 space = 6°. Angle 90° = 15 spaces. 3:00 = 15 spaces (90/6).

Basic · exact hour

Q1. 3:00 pe dono sui ka angle?

Solution shuru

Step 1
H=3, M=0. θ = |30×3 − 5.5×0| = 90°.

Final answer — yahan khatam90°

Basic · minutes bhi

Q2. 3:20 pe angle?

Solution shuru

Step 1 — hour
30×3 + 0.5×20 = 90 + 10 = 100°.
Step 2 — minute
6×20 = 120°.
Step 3
|100 − 120| = 20°. Formula: |30×3 − 5.5×20| = |90 − 110| = 20°. Same.

Final answer — yahan khatam20°

Basic

Q3. 6:00 pe angle?

Solution shuru

Step 1
|30×6 − 0| = 180°.

Final answer — yahan khatam180°

Medium

Q4. 2:30 pe chhota angle?

Solution shuru

Step 1
θ = |30×2 − 5.5×30| = |60 − 165| = 105°.
Step 2
105 < 180, yahi chhota. (360−105=255, bada wala.)

Final answer — yahan khatam105°

4. Kab milengi / 90° / 180°

Relative speed = 6 − 0.5 = 5.5° per minute (minute hand tez).

H baje ke baad, M minutes par:
Chipakna (0°): M = 30H / 5.5 = 60H / 11
Saamne (180°): M = (30H ± 180) / 5.5
Samkon (90°): M = (30H ± 90) / 5.5
M 0 se 60 ke beech hona chahiye. Jo na aaye, woh case mar.

Medium · together

Q5. 4 aur 5 baje ke beech sui kab chipakengi?

Solution shuru

Step 1
H=4. M = 60×4 / 11 = 240/11 = 21 ⁹/11 minutes.
Step 2
21 + 9/11 min. Time: 4 : 21 ⁹/11.

Final answer — yahan khatam4 : 21 9/11

Medium · 180°

Q6. 3 aur 4 ke beech kab sui seedhi (180°) honge?

Solution shuru

Step 1
H=3. 5.5M = 30×3 ± 180 = 90+180=270, ya 90−180=−90 (band).
Step 2
M = 270 / 5.5 = 540/11 = 49 ¹/11.

Final answer — yahan khatam3 : 49 1/11

5. 12 ghante mein kitni baar

Kaam	12 hours	24 hours	Yaad
Chipak (0°)	11	22	11–1 ke beech sirf 12 baje. 12 baar nahi.
Saamne (180°)	11	22	3–5 ke beech ek miss — pattern same 11.
90°	22	44	Har hour 2, lekin 2 hour mein 1 miss. 24 nahi.

“Har hour 2 baar 90° = 24” mat likhna. 2–4 aur 8–10 ke aas-paas ek-ek baar skip. Exam answer 22 (12 hour).

Basic · count

Q7. 12 baje se 12 baje (12 hours) sui kitni baar milengi?

Solution shuru

Step 1
Har hour-gap mein ek baar. 11 baje ke baad agla milna 12:00, phir 1 ke dauran nahi — 11–1 ke beech do nahi, ek. Isliye 12 nahi, 11.

Final answer — yahan khatam11

6. Mirror mein time

Vertical glass. 12 aur 6 same jagah, 3↔9 palat. Time nikalne ka shortcut:

Mirror time = 11:60 − diya hua time.
Example: 3:20 → 11:60 − 3:20 = 8:40.
Exact hour: 3:00 → 11:60 − 3:00 = 8:60 = 9:00 (ya 12:00 − 3:00).

Check: 12 ka mirror 12, 6 ka 6. 2 ka mirror 10, 4 ka 8, 5 ka 7.

Basic · mirror

Q8. Clock 3:20 dikha rahi. Mirror mein kya time?

Solution shuru

Step 1
11:60 − 3:20. Hours 11−3=8, minutes 60−20=40.

Final answer — yahan khatam8:40

7. Tez / sust ghadi

Do level: (1) sirf “5 min aage/peeche” — add/subtract. (2) har hour itna gain/lose — ratio.

Offset: 5 min fast + dikha 4:00 ⇒ asli 3:55. Slow ⇒ asli aage.
Gain/lose per hour: sahi 60 min mein clock 60±gain chalti.
Clock ke T minutes dikhe to asli = T × (60 / clock-speed).

Tez: clock-speed > 60 (jaise +5 ⇒ 65). Sust: < 60 (jaise −5 ⇒ 55).

Basic · offset

Q9. Ghadi 10 min sust hai. Woh 2:00 dikha rahi. Sahi time?

Solution shuru

Step 1
Sust = peeche. Asli aage: 2:00 + 10 min = 2:10.

Final answer — yahan khatam2:10

Pro · gain

Q10. Sahi 12:00 pe set. Har 60 sahi minutes mein 5 min gain (clock 65 dikhati). Jab clock 3:00 dikhe, sahi time kya (12 se)?

Solution shuru

Step 1 — ratio
65 clock min = 60 asli. Clock 3 hour = 180 clock min.
Step 2
Asli = 180 × 60/65 = 10800/65 = 2160/13 min = 166 ²/13 min.
Step 3
166 min = 2 hour + 46 min, plus 2/13 min. 12 se: 2:46 2/13.

Final answer — yahan khatam2 : 46 2/13

8. Pro checklist

Minutes hain to hour hand 0.5M aage — mat bhoolna.
θ = |30H − 5.5M|, phir chhota: min(θ, 360−θ).
M = 60H/11 chipakne pe. M>60 ho to us hour mein nahi.
12 hour: milna 11, 90° → 22.
Mirror: 11:60 − time.
Fast: asli peeche. Slow: asli aage. Gain/lose pe ratio.

9. Practice

Pehle khud socho, phir neeche solution kholo. Q1–Q10 yahan nahi dohraaye.

Basic

Practice 1. 12:00 pe angle?

Solution shuru

Step 1
Dono 12 pe. 0°.

Final answer — yahan khatam0°

Basic

Practice 2. 4:00 pe angle?

Solution shuru

Step 1
|30×4 − 0| = 120°.

Final answer — yahan khatam120°

Medium

Practice 3. 5:15 pe chhota angle?

Solution shuru

Step 1
θ = |30×5 − 5.5×15| = |150 − 82.5| = 67.5°.

Final answer — yahan khatam67.5°

Basic

Practice 4. 9:00 pe angle?

Solution shuru

Step 1
|30×9| = 270. Chhota = 360−270 = 90°.

Final answer — yahan khatam90°

Medium

Practice 5. 7 aur 8 ke beech sui kab milengi?

Solution shuru

Step 1
M = 60×7 / 11 = 420/11 = 38 ²/11.

Final answer — yahan khatam7 : 38 2/11

Medium

Practice 6. 5:40 pe chhota angle?

Solution shuru

Step 1
|30×5 − 5.5×40| = |150 − 220| = 70°.

Final answer — yahan khatam70°

Medium

Practice 7. Clock 10:10. Mirror time?

Solution shuru

Step 1
11:60 − 10:10 = 1:50.

Final answer — yahan khatam1:50

Basic

Practice 8. Ghadi 8 min tez. 6:00 dikha rahi. Sahi time?

Solution shuru

Step 1
Tez = aage. Asli peeche: 6:00 − 8 = 5:52.

Final answer — yahan khatam5:52

Pro

Practice 9. 24 hours mein sui kitni baar milengi?

Solution shuru

Step 1
12 hour mein 11. 24 mein 22. (12 midnight aur 12 noon dono count, lekin 24h window mein 22 events.)

Final answer — yahan khatam22

Pro

Practice 10. 12 hours mein kitni baar 90° (right angle)?

Solution shuru

Step 1
Har hour roughly 2, 24 nahi — 2 skips. Answer 22.

Final answer — yahan khatam22

10. Itna kaafi hai kya?

Agar tum:

|30H − 5.5M| se angle nikaal sako, 180 se bada ho to 360-minus
chipakne ka 60H/11 yaad ho
11 / 22 / 22 wale counts rat ke na, skip ki wajah samajh ke
mirror 11:60-minus, fast/slow offset, gain pe ratio

to JA/CA-II ke clock sawaal basic se pro tak attempt ho sakte hain.

Agle topic: Analogy.