Clock & Calendar
Key Concepts & Formulas
5-7 Essential Concepts for Clock & Calendar:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Minute Hand Speed | Moves 6° per minute (360°÷60) |
| 2 | Hour Hand Speed | Moves 0.5° per minute (30°÷60) |
| 3 | Relative Speed | Minute hand gains 5.5° per minute over hour hand |
| 4 | Odd Days | Remainder when total days divided by 7 |
| 5 | Leap Year Rule | Divisible by 4, except centuries (must be divisible by 400) |
| 6 | Month Codes | Jan=0, Feb=3, Mar=3, Apr=6, May=1, Jun=4, Jul=6, Aug=2, Sep=5, Oct=0, Nov=3, Dec=5 |
| 7 | Century Codes | 1600-1699=6, 1700-1799=4, 1800-1899=2, 1900-1999=0, 2000-2099=6 |
Essential Formulas
| Formula | Usage |
|---|---|
| Angle = | 30H - 5.5M |
| Odd days calculation | To find day of week for any given date |
| Total odd days = (Year code + Month code + Date + Century code) mod 7 | For calendar problems |
10 Practice MCQs
Q1. What is the angle between the hands at 3:00 PM? A) 90° B) 60° C) 120° D) 30°
Answer: A) 90°
Solution: Using formula: Angle = |30H - 5.5M| At 3:00, H=3, M=0 Angle = |30×3 - 5.5×0| = |90 - 0| = 90°
Shortcut: At exact hours, multiply hour by 30°
Concept: Clock & Calendar - Basic angle calculation
Q2. If January 1, 2024 is Monday, what day is January 8, 2024? A) Sunday B) Monday C) Tuesday D) Wednesday
Answer: B) Monday
Solution: Days difference = 8 - 1 = 7 days 7 days = 1 week = 0 odd days Same day: Monday
Shortcut: Difference of 7 days = same day of week
Concept: Clock & Calendar - Basic calendar calculation
Q3. How many times do the hands coincide in 12 hours? A) 11 B) 12 C) 22 D) 24
Answer: A) 11
Solution: Hands coincide when angle = 0° First coincidence: ~1:05 Last coincidence: ~11:55 Total: 11 times in 12 hours
Shortcut: 11 times in 12 hours, 22 times in 24 hours
Concept: Clock & Calendar - Coincidence of hands
Q4. A train leaves at 2:15 PM. What angle do the clock hands make at departure? A) 22.5° B) 30° C) 37.5° D) 45°
Answer: A) 22.5°
Solution: H = 2, M = 15 Angle = |30×2 - 5.5×15| = |60 - 82.5| = 22.5°
Shortcut: Remember 5.5° per minute difference
Concept: Clock & Calendar - Angle at specific time
Q5. If March 15, 2023 is Wednesday, what day is April 15, 2023? A) Friday B) Saturday C) Sunday D) Monday
Answer: B) Saturday
Solution: March has 31 days Days from March 15 to April 15 = 31 days Odd days = 31 mod 7 = 3 days Wednesday + 3 days = Saturday
Shortcut: 31 days = 4 weeks + 3 days
Concept: Clock & Calendar - Month transition
Q6. At what time between 4 and 5 o'clock are the hands at right angle? A) 4:05 B) 4:10 C) 4:15 D) 4:20
Answer: A) 4:05
Solution: For 90° angle: |30×4 - 5.5M| = 90 |120 - 5.5M| = 90 5.5M = 30 or 210 M = 5.45 or 38.18 First time: ~4:05
Shortcut: Use 5.5M = |30H ± 90|
Concept: Clock & Calendar - Right angle timing
Q7. A station clock shows 8:24. What is the reflex angle? A) 144° B) 216° C) 288° D) 72°
Answer: B) 216°
Solution: Angle = |30×8 - 5.5×24| = |240 - 132| = 108° Reflex angle = 360° - 108° = 252°
Shortcut: Reflex = 360° - smaller angle
Concept: Clock & Calendar - Reflex angle calculation
Q8. If August 15, 2021 is Sunday, what day is August 15, 2022? A) Sunday B) Monday C) Tuesday D) Wednesday
Answer: B) Monday
Solution: 2022 is not a leap year Total days = 365 Odd days = 365 mod 7 = 1 Sunday + 1 day = Monday
Shortcut: Non-leap year = +1 day, leap year = +2 days
Concept: Clock & Calendar - Year transition
Q9. A train journey starts at 11:40 AM and ends at 12:25 PM. Through what total angle does the minute hand turn? A) 270° B) 315° C) 270° D) 210°
Answer: A) 270°
Solution: Duration = 45 minutes Minute hand speed = 6° per minute Total angle = 45 × 6 = 270°
Shortcut: 45 minutes = ¾ circle = 270°
Concept: Clock & Calendar - Minute hand movement
Q10. If January 26, 2023 is Thursday, what day is January 26, 2024? A) Thursday B) Friday C) Saturday D) Sunday
Answer: B) Friday
Solution: 2024 is a leap year Total odd days = 366 mod 7 = 2 Thursday + 2 days = Saturday But 2023 is not leap, so +1 day Thursday + 1 = Friday
Shortcut: Check if Feb 29 falls in period
Concept: Clock & Calendar - Leap year calculation
5 Previous Year Questions
PYQ 1. What is the angle between the hands at 5:30? [RRB NTPC 2021 CBT-1]
Answer: B) 15°
Solution: H = 5, M = 30 Angle = |30×5 - 5.5×30| = |150 - 165| = 15°
Exam Tip: Always subtract smaller from larger, take absolute value
Concept: Clock & Calendar - Angle calculation
PYQ 2. If March 1, 2020 is Sunday, what day is March 1, 2021? [RRB Group D 2022]
Answer: C) Monday
Solution: 2020 is leap year (Feb 29 included) Total days = 366 Odd days = 366 mod 7 = 2 Sunday + 2 days = Tuesday
Exam Tip: 2020 is leap year, so add 2 days
Concept: Clock & Calendar - Leap year transition
PYQ 3. At what time between 7 and 8 o'clock do the hands coincide? [RRB ALP 2018]
Answer: A) 7:38
Solution: For coincidence: 30H = 5.5M 30×7 = 5.5M 210 = 5.5M M = 38.18 minutes
Exam Tip: Use 30H = 5.5M for coincidence
Concept: Clock & Calendar - Coincidence timing
PYQ 4. A clock loses 5 minutes every hour. If set right at 6 AM, what time shown at actual 6 PM? [RRB JE 2019]
Answer: B) 5:00 PM
Solution: Duration = 12 hours Clock loses: 5 × 12 = 60 minutes = 1 hour Shown time = 6 PM - 1 hour = 5 PM
Exam Tip: Calculate total minutes lost first
Concept: Clock & Calendar - Faulty clock
PYQ 5. What day is January 26, 2025? [RPF SI 2019]
Answer: A) Sunday
Solution: Use formula: Total odd days = (Year code + Month code + Date + Century code) mod 7 Year code for 25 = 25 + 6 = 31 mod 7 = 3 Month code for Jan = 0 Date = 26 mod 7 = 5 Century code = 0 (1900-1999) Total = (3 + 0 + 5 + 0) mod 7 = 8 mod 7 = 1 Day = Sunday (0=Sunday, 1=Monday… but here 1=Sunday) Actually: 1 = Sunday
Exam Tip: 0=Sunday, 1=Monday in standard coding
Concept: Clock & Calendar - Day calculation
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Right angle times | 5.5M = | 30H ± 90 |
| Leap year check | Divisible by 4, not by 100 unless by 400 | 2000: leap, 1900: not leap |
| Month day addition | 31 days = +3, 30 days = +2, Feb = +0/+1 | Mar to Apr = +3 days |
| Century codes | 1600s=6, 1700s=4, 1800s=2, 1900s=0, 2000s=6 | 2023 uses 6 |
| Quick angle check | Hour × 30 - minutes × 5.5 | 4:15 = 120 - 82.5 = 37.5° |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Sign error in angle formula | Forgetting absolute value | Always take |
| Wrong leap year for century years | Assuming all ÷4 are leap | Check ÷400 for century years |
| Month code confusion | Mixing up month codes | Memorize: JFM=0,3,3 AMJ=6,1,4 JAS=6,2,5 OND=0,3,5 |
| Counting odd days | Including current day | Count days BETWEEN dates |
| 24-hour angle > 180° | Taking smaller angle | Reflex angle = 360° - smaller angle |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Minute hand speed | 6° per minute |
| Hour hand speed | 0.5° per minute |
| Relative speed | 5.5° per minute |
| Leap year rule | ÷4, not ÷100 unless ÷400 |
| January code | 0 |
| February code | 3 |
| Century code 1900s | 0 |
| Century code 2000s | 6 |
| Odd days in 365 days | 1 |
| Odd days in 366 days | 2 |
Topic Connections
Direct Link:
- Time & Work: Calculating actual working hours with faulty clocks
- Speed & Distance: Train schedules using clock calculations
- Data Interpretation: Calendar-based data analysis
Combined Questions:
- Clock angle + Speed problems (train departure times)
- Calendar + Age calculations (birthday on specific day)
- Time zone + Clock problems (Indian Railway timings)
Foundation For:
- Advanced reasoning puzzles
- Scheduling and optimization problems
- Real-time system calculations in technical exams
BETA
