Calendar Problems in Reasoning: 20 Unique Questions with Solutions

The calendar is an essential topic in logical reasoning, especially for competitive exams like SSC CGL, Banking, and UPSC. It includes questions related to finding the day of the week, leap years, odd days, and other calendar-based problems. In this blog, we will explore 20 unique calendar problems with detailed explanations to help you master this topic.

1. Finding the Day of a Given Date

Question: What was the day of the week on 15th August 1947?

Solution:

Base year: 1900 (1st Jan 1900 was a Monday)
Counting odd days:
- 1900-1947 = 47 years (11 leap years + 36 normal years) → (11×2 + 36×1) = 58 odd days → 58 ÷ 7 = 2 odd days
- January to August 15th, 1947 → 3 + 0 + 3 + 2 + 3 + 2 + 3 + 5 = 21 odd days → 21 ÷ 7 = 0 odd days
- Total odd days = 2
- Monday + 2 days = Friday

2. Leap Year Identification

Question: Which of the following is a leap year? A) 1700
B) 1800
C) 1900
D) 2000

Solution: A year is a leap year if it is divisible by 4, but if it is a century year, it must be divisible by 400. Only 2000 is a leap year.

Answer: D) 2000

3. Finding Odd Days

Question: How many odd days are there in 400 years?

Solution:

1 normal year = 365 days = 1 odd day
1 leap year = 366 days = 2 odd days
400 years = 100 leap years + 300 normal years
Odd days = (100×2 + 300×1) = 200 + 300 = 500 days
500 ÷ 7 = 0 odd days

Answer: 0 odd days

4. Next Same Calendar Year

Question: When will the calendar of 2024 repeat?

Solution:

Leap years repeat after 28 years.
The next year with the same calendar as 2024 will be 2052.

Answer: 2052

5. Previous Same Calendar Year

Question: Which year had the same calendar as 2023?

Solution:

Normal years repeat after 6 or 11 years.
The last same calendar was in 2017.

Answer: 2017

6. First Day of Any Century

Question: What is the first day of the 21st century (1st January 2001)?

Solution:

1st Jan 1901 was Tuesday.
100 years = 0 odd days.
So, 1st Jan 2001 is also Monday.

Answer: Monday

7. Day Calculation with Odd Days

Question: If today is Wednesday, what day will it be after 60 days?

Solution:

60 ÷ 7 = 4 odd days.
Wednesday + 4 days = Sunday

Answer: Sunday

8. Last Day of a Century

Question: What is the last day of the 20th century (31st December 2000)?

Solution:

31st Dec 1899 was Sunday.
100 years = 0 odd days.
So, 31st Dec 2000 is also Sunday.

Answer: Sunday

9. Repeating Calendar within a Decade

Question: When will the calendar of 2022 repeat?

Solution:

2022 is a normal year, and such years repeat after 6 or 11 years.
The next similar calendar will be in 2033.

Answer: 2033

10. Counting Fridays in a Year

Question: How many Fridays are there in a leap year?

Solution:

366 days = 52 weeks + 2 extra days.
These extra days can make 53 Fridays if the year starts on a Thursday or Friday.

Answer: 52 or 53

11. Odd Days in a Month

Question: How many odd days are there in February of a leap year?

Solution:

February (leap year) = 29 days
29 ÷ 7 = 1 odd day

Answer: 1 odd day

12. Identifying a Leap Century Year

Question: Which of the following is a leap century year? A) 1600
B) 1700
C) 1800
D) 1900

Solution: Only centuries divisible by 400 are leap years.

Answer: A) 1600

13. Number of Sundays in a Year

Question: How many Sundays are there in a normal year?

Solution:

365 days = 52 weeks + 1 extra day
Extra day can be any weekday, so Sundays remain 52 or 53.

Answer: 52 or 53

14. Checking Leap Year

Question: Is the year 2028 a leap year?

Solution:

2028 ÷ 4 = yes, so it’s a leap year.

Answer: Yes

15. 1000th Day from Today

Question: If today is Monday, what day will it be after 1000 days?

Solution:

1000 ÷ 7 = 6 odd days
Monday + 6 = Sunday

Answer: Sunday

16. Month Having Same Calendar as August

Question: Which month has the same calendar as August in a non-leap year?

Answer: February

17. Counting Leap Years Between Two Dates

Question: How many leap years are there between 1901 and 2000?

Solution:

Leap years: 1904, 1908, ..., 2000
Total = 25

Answer: 25

18. 365th Day from Today

Question: If today is Monday, what will be the day after 365 days?

Solution:

365 ÷ 7 = 1 odd day
Monday + 1 = Tuesday

Answer: Tuesday

19. Century Not a Leap Year

Question: Which of the following is not a leap year? A) 1800
B) 2000
C) 1600
D) 2400

Answer: A) 1800

20. Calendar Repetition Rule

Question: After how many years does a leap year repeat?

Solution: 28 years.

Answer: 28 years

These 20 questions cover all important concepts of calendar problems in reasoning. Keep practicing to master this topic!