The calendar for the year 2025 is same for
- (a) 2029
- (b) 2030
- (c) 2031 ✓ UPSC's answer
- (d) 2033
Why the answer is (c)
• A calendar repeats when the total number of days between the two years is a multiple of 7, meaning the 'odd days' (remainder of total days divided by 7) must be zero.
• From 2025 to 2031, there are 6 years in between: 2025, 2026, 2027, 2028, 2029, and 2030.
• Among these, 2028 is a leap year (divisible by 4), contributing 2 odd days, while the other 5 common years contribute 1 odd day each.
• The total odd days are calculated as (5 × 1) + (1 × 2) = 7, which is exactly divisible by 7, resulting in 0 net odd days.
• Since the net odd days are zero, the days of the week for every date in 2031 will align perfectly with 2025, making the calendars identical.
Why the other options are wrong
- (a) 2029
- The period from 2025 to 2029 contains 4 common years and 1 leap year (2028), resulting in 6 odd days, so the calendar shifts by 6 days.
- (b) 2030
- The period from 2025 to 2030 contains 4 common years and 1 leap year (2028), resulting in 6 odd days, so the calendar shifts by 6 days.
- (d) 2033
- The period from 2025 to 2033 contains 7 common years and 1 leap year (2028), resulting in 9 odd days (or 2 net odd days), so the calendar shifts by 2 days.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.