Question Details

The calendar for the year 2025 is same for:

Options

A

2029

B

2030

C

2031

D

2033

Show Answer

Correct Answer :

Option C

2031

Solution :

The correct option is 2031.

To find the year that has the same calendar as the year 2025, we need to understand how the calendar repeats. Two years have the same calendar if they meet two conditions:
1. Both years are of the same type (either both are ordinary years, or both are leap years).
2. The number of odd days (extra days beyond complete weeks) accumulated between the two years is a multiple of 7.

Let's analyze the year 2025:
Since 2025 is not divisible by 4, it is an ordinary year (containing 365 days). An ordinary year has 52 weeks and 1 odd day (3651mod7). A leap year contains 366 days, which corresponds to 52 weeks and 2 odd days (3662mod7).

We will count the number of accumulated odd days starting from 2025 onwards:

- Year 2025 (Ordinary year) = 1 odd day
- Year 2026 (Ordinary year) = 1 odd day
- Year 2027 (Ordinary year) = 1 odd day
- Year 2028 (Leap year) = 2 odd days
- Year 2029 (Ordinary year) = 1 odd day
- Year 2030 (Ordinary year) = 1 odd day

Let's sum the odd days from the beginning of 2025 up to the end of 2030 (which is the start of 2031):
Total odd days = 1+1+1+2+1+1=7 odd days.

Since 7 odd days make exactly 1 week, the calendar for the year 2031 will start on the same day of the week as 2025.
Now we check if 2031 is also an ordinary year: 2031 is not divisible by 4, so it is indeed an ordinary year.

Since both 2025 and 2031 are ordinary years and the sum of odd days between them is a multiple of 7, the calendar for the year 2025 is the same as the calendar for the year 2031.

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