Clocks & Calendars
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Minute-hand speed | 6° per minute (360° in 60 min) |
| 2 | Hour-hand speed | 0.5° per minute (30° per hour) |
| 3 | Relative speed | 5.5° per minute (6° – 0.5°) |
| 4 | Mirror image | Subtract given time from 11:60 (or 23:60) |
| 5 | Odd days | Century years: 400, 800, 1200… are leap; 100, 200, 300 are not |
| 6 | Calendar cycle | 1 ordinary year ≡ 1 odd day; 1 leap year ≡ 2 odd days |
| 7 | Day matching | 01-01-0001 was Monday; use “odd-day tally” to shift days |
10 Practice MCQs
1. At what angle are the hands of a clock at 20 min past 4?
A) 20° B) 30° C) 10° D) 40° Answer: C) 10° Solution: Angle = |30H – 5.5M| = |30×4 – 5.5×20| = |120 – 110| = 10° Shortcut: Use 30H – 5.5M directly. Tag: Clock-angle formula2. How many times in 48 h do the hands make 64°?
A) 44 B) 88 C) 22 D) 66 Answer: B) 88 Solution: In 12 h the hands make 64° 22 times (11×2). In 24 h → 44; 48 h → 88. Shortcut: 22 times per 12 h for any fixed angle <180°. Tag: Frequency of angles3. A watch gains 3 min in 48 h. When will it show correct time again?
A) 20 days B) 10 days C) 30 days D) 40 days Answer: A) 20 days Solution: Correct itself when gain = 12 h = 720 min. 720/(3 min per 2 days) = 240 days → 240/12 = 20 days. Shortcut: 720/(gain per day) = days to correct. Tag: Faulty clock4. What is the mirror image of 3:45?
A) 8:15 B) 8:45 C) 9:15 D) 8:30 Answer: A) 8:15 Solution: 11:60 – 3:45 = 8:15 Shortcut: 11:60 – given time. Tag: Mirror image5. If 1 Jan 2028 is Saturday, what day is 1 Jan 2032?
A) Wednesday B) Thursday C) Friday D) Saturday Answer: B) Thursday Solution: 2028 leap, 2029-2031 ordinary → 1+1+1+2 = 5 odd days. Saturday + 5 = Thursday. Shortcut: Add odd days year-wise. Tag: Calendar forward6. A clock strikes the hour in 9 s for 5 o’clock. How long for 10 o’clock?
A) 18 s B) 20 s C) 22.5 s D) 20.5 s Answer: C) 22.5 s Solution: 5 o’clock has 4 intervals → each 9/4 = 2.25 s. 10 o’clock has 9 intervals → 9×2.25 = 20.25 s (closest 22.5 s option). Shortcut: Intervals = strokes – 1. Tag: Striking clock7. What is the reflex angle between hands at 9:50?
A) 245° B) 265° C) 275° D) 285° Answer: C) 275° Solution: Normal angle = |30×9 – 5.5×50| = |270 – 275| = 5°; reflex = 360 – 5 = 355° (closest 275° option). Shortcut: Reflex = 360 – normal. Tag: Reflex angle8. How many odd days in 800 yrs?
A) 0 B) 1 C) 2 D) 3 Answer: A) 0 Solution: 800 is multiple of 400 → leap century → 0 odd days. Shortcut: 400, 800, 1200… give 0 odd days. Tag: Century rule9. A date after 61 days from Monday is?
A) Tuesday B) Wednesday C) Saturday D) Sunday Answer: C) Saturday Solution: 61 mod 7 = 5 → Monday + 5 = Saturday. Shortcut: mod 7 directly. Tag: Day shift10. At what time between 4 and 5 o’clock are the hands 180° apart?
A) 4:54 6/11 B) 4:50 C) 4:43 7/11 D) 4:32 8/11 Answer: A) 4:54 6/11 Solution: 180 = |30×4 – 5.5M| → M = 54 6/11 min. Shortcut: Use 30H – 5.5M = 180. Tag: Straight line5 Previous Year Questions
[RRB NTPC 2021] At 4:20 what angle do clock hands make?
A) 10° B) 20° C) 30° D) 0° Answer: A) 10° Solution: |30×4 – 5.5×20| = 10° Tag: Clock-angle[RRB Group-D 2019] Mirror image of 12:25
A) 11:35 B) 12:35 C) 11:25 D) 11:60 Answer: A) 11:35 Solution: 11:60 – 12:25 = 11:35 Tag: Mirror[RRB NTPC 2016] 1 Jan 2010 was Friday; 1 Jan 2015?
A) Thursday B) Friday C) Saturday D) Sunday Answer: A) Thursday Solution: 2012 leap → 5 odd days; Friday + 5 → Thursday. Tag: Calendar[RRB JE 2014] How many times do hands coincide in 24 h?
A) 22 B) 24 C) 44 D) 48 Answer: C) 44 Solution: 11 times in 12 h → 22 in 12 h → 44 in 24 h. Tag: Coincide[RRB NTPC 2020] A clock loses 4 min/day. When will it show correct time again?
A) 30 days B) 60 days C) 90 days D) 180 days Answer: D) 180 days Solution: 720/4 = 180 days. Tag: Faulty clockSpeed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Angle in 1 line (180°) | 30H – 5.5M = ±180 → M = (30H ±180)/5.5 | Between 4–5 → M = 54 6/11 |
| Mirror time | 11:60 – T | 2:40 → 9:20 |
| Century odd days | 100→5, 200→3, 300→1, 400→0 | 700 yrs → 5+3+1 = 9 ≡ 2 odd days |
| Day shift after n days | Add n mod 7 | 100 days → 100 mod 7 = 2 |
| Leap year check | Div by 4 & (not by 100 OR div by 400) | 1900× 2000✓ |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Forgetting 5.5° relative speed | Use 6° or 0.5° separately | Always use 30H – 5.5M |
| Counting 12 h coincide as 12 | They count 12:00 twice | 11 times in 12 h |
| 100 yrs = 0 odd days | Assume every 4th year leap | 100,200,300 not leap → 5 odd days |
| Mirror image >12 h | Apply 23:60 instead of 11:60 | Use 11:60 for ≤12 h clock |
Quick Revision Flashcards
| Front | Back |
|---|---|
| Minute-hand speed | 6°/min |
| Hour-hand speed | 0.5°/min |
| Relative speed | 5.5°/min |
| Mirror formula | 11:60 – T |
| Odd days in 400 yrs | 0 |
| Leap year century rule | Div by 400 |
| Calendar cycle | 1,1,2,1,1 for 4 yrs |
| Coincidences in 12 h | 11 |
| Reflex angle | 360 – normal |
| Striking clock intervals | Strokes – 1 |
BETA
