Calendar: Odd Days, Day of the Week and Repeating Calendars
Calendar: Odd Days, Day of the Week and Repeating Calendars
Calendar questions run on "odd days": the days left over after complete weeks. Add up odd days from a known reference and the remainder after dividing by 7 tells you the weekday. NTPC-style questions ask the day on a date, the day on the same date in another year, which year repeats a calendar, and how many times a weekday occurs.
1. Odd-Day Tables
| Period | Odd days |
|---|---|
| Normal year (365 days) | 1 |
| Leap year (366 days) | 2 |
| 100 years | 5 |
| 200 years | 3 |
| 300 years | 1 |
| 400 years | 0 |
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Odd days | 3 | 0 (1 in leap) | 3 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 3 |
| Remainder | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Day | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
Leap year: divisible by 4; a century year only if divisible by 400 (2000 yes, 1900 no)
Same date one year later: +1 day (normal) or +2 days if 29 February falls in between
A normal year's calendar repeats after 6 years (the year after a leap year) or 11 years (the other two normal years); a leap year's calendar repeats after 28 years
A normal year begins and ends on the same weekday; a leap year ends one day later than it began
✗ 10 March 2024 to 10 March 2025 adds 2 days because 2024 is a leap year | ✓ 29 February 2024 is before 10 March 2024, so only 365 days pass: +1
✗ 1900 was a leap year | ✓ Century years must be divisible by 400; 1900 was not
हिंदी नोट: कैलेंडर प्रश्नों में विषम दिन जोड़िए और 7 से भाग देकर शेषफल से दिन पहचानिए (0 = रविवार)। सामान्य वर्ष में 1 और लीप वर्ष में 2 विषम दिन होते हैं। शताब्दी वर्ष तभी लीप है जब 400 से विभाज्य हो।
Exam Pointer: These patterns had no verified NTPC shift in our check (calendar pages found carried other exam labels or none) and are tagged syllabus-based. Calendar is part of the NTPC reasoning syllabus and appears in CBT-2 as well.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Day of the week from a known day
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. 1 January 2025 was a Wednesday. What day was 1 January 2026?
2025 is a normal year, 1 odd day: Wednesday + 1 = Thursday.
Answer: Thursday
EXAMATLAS LEVEL
Q. 26 January 2026 is a Monday. What day of the week is 15 August 2026?
Days after 26 January: 5 (rest of January) + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 201. 201 = 28 weeks + 5 days, so Monday + 5 = Saturday.
Answer: Saturday
Pattern 2: Day of the week on any date (odd-day method)
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. 10 March 2024 was a Sunday. What day was 10 March 2025?
The year between them contains no 29 February (that came before 10 March 2024), so 365 days pass: Sunday + 1 = Monday.
Answer: Monday
EXAMATLAS LEVEL
Q. What day of the week was 15 August 1947?
Up to 1600: 0 odd days. 1601 to 1900 (300 years): 1. 1901 to 1946: 11 leap years and 35 normal years give 22 + 35 = 57, which is 1 odd day. 1947 to 15 August: 3 + 0 + 3 + 2 + 3 + 2 + 3 + 15 = 31, which is 3 odd days. Total 0 + 1 + 1 + 3 = 5: Friday.
Answer: Friday
Pattern 3: Repeating calendars
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Which is the next year with the same calendar as 2023?
Add odd days from 2023 until the total is a multiple of 7, with the target year also non-leap: 2023 (1), 2024 (2), 2025 (1), 2026 (1), 2027 (1), 2028 (2), 2029 (1), 2030 (1), 2031 (1), 2032 (2), 2033 (1) make 14. So 2034 matches, and it is a normal year.
Answer: 2034
EXAMATLAS LEVEL
Q. Which is the next year with the same calendar as 2024, and as 2026?
A leap year repeats after 28 years: 2052. For 2026, adding odd days 2026 (1), 2027 (1), 2028 (2), 2029 (1), 2030 (1), 2031 (1), 2032 (2), 2033 (1), 2034 (1), 2035 (1), 2036 (2) gives 14, so 2037, which is a normal year, repeats it.
Answer: 2052; 2037
Pattern 4: Weekdays occurring 5 or 53 times
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A 31-day month begins on a Saturday. How many Sundays does it have?
31 days = 4 weeks + 3 days, so the first three weekdays of the month (Saturday, Sunday, Monday) occur 5 times.
Answer: 5
EXAMATLAS LEVEL
Q. A leap year begins on a Thursday. Which weekdays occur 53 times in it, and on which day does it end?
366 = 52 weeks + 2 days, so the first two weekdays occur 53 times: Thursday and Friday. The year ends on Friday.
Answer: Thursday and Friday; Friday
60-Second Revision
- Odd days: normal year 1, leap year 2; 100 years 5, 400 years 0.
- Remainder 0 = Sunday, 1 = Monday ... 6 = Saturday.
- Count 29 February only if it lies between the two dates.
- Leap-year calendars repeat after 28 years.