MPESB Group · Bite-size lessons
Calendar and Clock
About 6 min · Reasoning and Aptitude · English
Time worked out from the lesson's 404 words at 150 words a minute, plus a minute for each question.
Calendar and Clock problems test your ability to perform time-based calculations quickly and accurately. The calendar section requires you to find the day of the week for any given date, count odd days, or determine leap years. The clock section focuses on calculating angles between hands and finding times when hands overlap or form specific angles.
Key ideas
- Odd Days: The remainder when total days are divided by 7. This determines how many days the week shifts forward from a reference day.
- Leap Year Rule: A year is a leap year if divisible by 4, except century years must be divisible by 400. So 2000 was a leap year, but 1900 was not.
- Ordinary Year vs Leap Year: Ordinary year = 365 days = 52 weeks + 1 odd day. Leap year = 366 days = 52 weeks + 2 odd days.
- Day Codes: Sunday = 0, Monday = 1, Tuesday = 2, Wednesday = 3, Thursday = 4, Friday = 5, Saturday = 6.
- Clock Hand Movement: The minute hand moves 360° in 60 minutes (6° per minute). The hour hand moves 360° in 12 hours (0.5° per minute or 30° per hour).
Watch out for
- Forgetting century leap year rule → Students mark 1900 as a leap year. Remember: 1700, 1800, 1900 were NOT leap years; 2000 WAS a leap year (divisible by 400).
- Confusing the angle formula → Some students use 30H + 5.5M. The correct formula is 30H − 5.5M (hour hand position minus minute hand position).
- Not adjusting for angles greater than 180° → If your calculated angle exceeds 180°, the actual angle is 360° minus that value. Examiners often give such options as traps.
Quick reference
- 400 years = 0 odd days (calendar repeats exactly)
- Angle formula: |30H − 5.5M| degrees
- Minute hand moves 6° per minute; hour hand moves 0.5° per minute
- Hands overlap 11 times in 12 hours, not 12 times
- Leap year test: Divisible by 4, but centuries must be divisible by 400
Check yourself: 3 questions
1. If 15th August 2023 is a Tuesday, what day of the week will be 15th August 2024?
2. What is the angle between the hour hand and the minute hand of a clock at 3:15?
3. At what time between 4 o'clock and 5 o'clock will the hands of a clock be at right angles (90 degrees) for the first time?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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