Case 2: Finding the Day When Year Is Same but Date and Month Are Different
In this type:
- Year remains same
- Date changes
- Month changes
Examples:
- If 10 January 2025 was Friday, what day was 25 May 2025?
- If 15 February 2024 was Monday, what day was 20 July 2024?
Since the year is the same, we do not calculate odd days from years.
Instead, we calculate odd days directly from:
- remaining days in the starting month
- complete months in between
- ending date
This method is very fast and commonly used in competitive exams.
Important Odd Days
Month With 31 Days
31 ÷ 7 = remainder 3
So:
31-day month = 3 odd days
Month With 30 Days
30 ÷ 7 = remainder 2
So:
30-day month = 2 odd days
February
28 ÷ 7 = remainder 0
So:
February = 0 odd days
Leap Year February
29 ÷ 7 = remainder 1
So:
Leap February = 1 odd day
Step-by-Step Method
Step 1
Find odd days remaining in the starting month.
Step 2
Add odd days of complete months in between.
Step 3
Add odd days of the ending date.
Step 4
Divide total odd days by 7.
Step 5
Move weekday according to the remainder.
Now let us understand with examples.
Example 1
If 10 January 2025 was Friday, what day was 25 May 2025?
Step 1: Remaining Days in January
January has 31 days.
Remaining days:
31 − 10 = 21
21 ÷ 7 = remainder 0
Odd days = 0
Step 2: Complete Months in Between
February = 0
March = 3
April = 2
Total:
0 + 3 + 2 = 5
Odd days = 5
Step 3: Ending Date
Date = 25
25 ÷ 7 = remainder 4
Odd days = 4
Step 4: Total Odd Days
0 + 5 + 4
= 9
9 ÷ 7 = remainder 2
Total odd days = 2
Step 5: Move Weekday
Given:
10 January 2025 = Friday
Move 2 days forward:
Saturday → 1
Sunday → 2
Answer:
25 May 2025 was Sunday.
Case 3: Finding the Day When Date, Month, and Year Are All Different
In this type:
- Date is different
- Month is different
- Year is different
Examples:
- If 10 January 2020 was Friday, what day was 25 May 2025?
- If 15 March 2018 was Monday, what day was 20 August 2023?
- If 5 April 2010 was Tuesday, what day was 30 September 2020?
Here everything changes:
- date
- month
- year
So we must combine the methods from Case 1 and Case 2.
Step-by-Step Method
Step 1
Calculate odd days from years.
Formula:
Total Years + Leap Years
Step 2
Find odd days remaining in the starting month.
Step 3
Add odd days of complete months in between.
Step 4
Add odd days of the ending date.
Step 5
Add all odd days.
Step 6
Divide by 7 and find the remainder.
Step 7
Move weekday according to the remainder.
This single method can solve most calendar questions.
Example 1
If 10 January 2020 was Friday, what day was 25 May 2025?
Step 1: Odd Days From Years
Years between:
2020
2021
2022
2023
2024
Total years = 5
Leap years:
2020
2024
Total leap years = 2
Odd days:
5 + 2 = 7
7 mod 7 = 0
Year odd days = 0
Step 2: Remaining Days in January
31 − 10 = 21
21 mod 7 = 0
Odd days = 0
Step 3: Complete Months
February = 0
March = 3
April = 2
Total:
0 + 3 + 2
= 5
Odd days = 5
Step 4: Ending Date
25 mod 7 = 4
Odd days = 4
Step 5: Total Odd Days
0 + 0 + 5 + 4
= 9
9 mod 7 = 2
Total odd days = 2
Step 6: Move Weekday
Given:
10 January 2020 = Friday
Move 2 days forward:
Saturday → 1
Sunday → 2
Answer:
25 May 2025 was Sunday.
Calendar Problems Practice MCQs
1. If 15 August 2010 was Sunday, what day was 15 August 2015?
A) Thursday
B) Friday
C) Saturday
D) Sunday
Answer: C) Saturday
Explanation:
Since the date and month are the same, we only calculate the odd days contributed by the years.
Years involved:
- 2010 = Normal Year = 1 odd day
- 2011 = Normal Year = 1 odd day
- 2012 = Leap Year = 2 odd days
- 2013 = Normal Year = 1 odd day
- 2014 = Normal Year = 1 odd day
Total odd days:
1 + 1 + 2 + 1 + 1 = 6
Move 6 days forward from Sunday:
- Monday = 1
- Tuesday = 2
- Wednesday = 3
- Thursday = 4
- Friday = 5
- Saturday = 6
Therefore, 15 August 2015 was Saturday.
2. If 10 January 2025 was Friday, what day was 25 May 2025?
A) Saturday
B) Sunday
C) Monday
D) Tuesday
Answer: B) Sunday
Explanation:
Since the year is the same, calculate odd days from the months and date.
Step 1: Remaining days in January
31 − 10 = 21 days
21 mod 7 = 0 odd days
Step 2: Complete months between January and May
February = 28 days = 0 odd days
March = 31 days = 3 odd days
April = 30 days = 2 odd days
Total = 0 + 3 + 2 = 5 odd days
Step 3: Days in May
25 mod 7 = 4 odd days
Step 4: Total odd days
0 + 5 + 4 = 9
9 mod 7 = 2 odd days
Step 5: Find the day
Friday + 2 days
- Saturday = 1
- Sunday = 2
Therefore, 25 May 2025 was Sunday.
3. If 26 January 2015 was Monday, what day was 26 January 2020?
A) Friday
B) Saturday
C) Sunday
D) Monday
Answer: C) Sunday
Explanation:
The date and month are the same, so calculate odd days from the years only.
Years involved:
- 2015 = Normal Year = 1 odd day
- 2016 = Leap Year = 2 odd days
- 2017 = Normal Year = 1 odd day
- 2018 = Normal Year = 1 odd day
- 2019 = Normal Year = 1 odd day
Total odd days:
1 + 2 + 1 + 1 + 1 = 6
Move 6 days forward from Monday:
- Tuesday = 1
- Wednesday = 2
- Thursday = 3
- Friday = 4
- Saturday = 5
- Sunday = 6
Therefore, 26 January 2020 was Sunday.
4. If 1 March 2017 was Wednesday, what day was 1 March 2021?
A) Sunday
B) Monday
C) Tuesday
D) Wednesday
Answer: B) Monday
Explanation:
Since the date and month are the same, we only need to calculate the odd days contributed by the years.
Years involved:
- 2017 = Normal Year = 1 odd day
- 2018 = Normal Year = 1 odd day
- 2019 = Normal Year = 1 odd day
- 2020 = Leap Year = 2 odd days
Total odd days:
1 + 1 + 1 + 2 = 5
Move 5 days forward from Wednesday:
- Thursday = 1
- Friday = 2
- Saturday = 3
- Sunday = 4
- Monday = 5
Therefore, 1 March 2021 was Monday.
5. If 5 February 2023 was Sunday, what day was 20 June 2023?
A) Monday
B) Tuesday
C) Wednesday
D) Thursday
Answer: B) Tuesday
Explanation:
Since the year is the same, calculate odd days from months and dates.
Step 1: Remaining days in February
28 − 5 = 23 days
23 mod 7 = 2 odd days
Step 2: Complete months between February and June
March = 31 days = 3 odd days
April = 30 days = 2 odd days
May = 31 days = 3 odd days
Total:
3 + 2 + 3 = 8 odd days
8 mod 7 = 1 odd day
Step 3: Days in June
20 mod 7 = 6 odd days
Step 4: Total odd days
2 + 1 + 6 = 9
9 mod 7 = 2 odd days
Step 5: Find the day
Sunday + 2 days
- Monday = 1
- Tuesday = 2
Therefore, 20 June 2023 was Tuesday.
6. If 10 January 2020 was Friday, what day was 10 January 2025?
A) Wednesday
B) Thursday
C) Friday
D) Saturday
Answer: C) Friday
Explanation:
Since the date and month are the same, calculate odd days from the years only.
Years involved:
- 2020 = Leap Year = 2 odd days
- 2021 = Normal Year = 1 odd day
- 2022 = Normal Year = 1 odd day
- 2023 = Normal Year = 1 odd day
- 2024 = Leap Year = 2 odd days
Total odd days:
2 + 1 + 1 + 1 + 2 = 7
7 mod 7 = 0
Step 2: Find the day
Friday + 0 days = Friday
Therefore, 10 January 2025 was Friday.
7. If 12 April 2018 was Thursday, what day was 12 April 2023?
A) Monday
B) Tuesday
C) Wednesday
D) Thursday
Answer: C) Wednesday
Explanation:
Since the date and month are the same, we only calculate odd days from the years.
Years involved:
- 2018 = Normal Year = 1 odd day
- 2019 = Normal Year = 1 odd day
- 2020 = Leap Year = 2 odd days
- 2021 = Normal Year = 1 odd day
- 2022 = Normal Year = 1 odd day
Total odd days:
1 + 1 + 2 + 1 + 1 = 6
Move 6 days forward from Thursday:
- Friday = 1
- Saturday = 2
- Sunday = 3
- Monday = 4
- Tuesday = 5
- Wednesday = 6
Therefore, 12 April 2023 was Wednesday.
8. If 8 March 2024 was Friday, what day was 25 July 2024?
A) Monday
B) Tuesday
C) Wednesday
D) Thursday
Answer: D) Thursday
Explanation:
Since the year is the same, calculate odd days from months and dates.
Step 1: Remaining days in March
31 − 8 = 23 days
23 mod 7 = 2 odd days
Step 2: Complete months between March and July
April = 30 days = 2 odd days
May = 31 days = 3 odd days
June = 30 days = 2 odd days
Total:
2 + 3 + 2 = 7 odd days
7 mod 7 = 0 odd days
Step 3: Days in July
25 mod 7 = 4 odd days
Step 4: Total odd days
2 + 0 + 4 = 6 odd days
Step 5: Find the day
Friday + 6 days
- Saturday = 1
- Sunday = 2
- Monday = 3
- Tuesday = 4
- Wednesday = 5
- Thursday = 6
Therefore, 25 July 2024 was Thursday.
9. If 20 June 2019 was Thursday, what day was 15 September 2022?
A) Monday
B) Tuesday
C) Wednesday
D) Thursday
Answer: D) Thursday
Explanation:
Date, month, and year are different, so calculate odd days from years, months, and dates.
Step 1: Odd days from years
- 2019 = Normal Year = 1 odd day
- 2020 = Leap Year = 2 odd days
- 2021 = Normal Year = 1 odd day
Total:
1 + 2 + 1 = 4 odd days
Step 2: Remaining days in June
30 − 20 = 10 days
10 mod 7 = 3 odd days
Step 3: Complete months
July = 31 days = 3 odd days
August = 31 days = 3 odd days
Total:
3 + 3 = 6 odd days
Step 4: Ending date
15 mod 7 = 1 odd day
Step 5: Total odd days
4 + 3 + 6 + 1 = 14
14 mod 7 = 0
Step 6: Find the day
Thursday + 0 days = Thursday
Therefore, 15 September 2022 was Thursday.
10. If 1 January 2021 was Friday, what day was 1 January 2026?
A) Tuesday
B) Wednesday
C) Thursday
D) Friday
Answer: C) Thursday
Explanation:
Since the date and month are the same, we only calculate odd days from the years.
Years involved:
- 2021 = Normal Year = 1 odd day
- 2022 = Normal Year = 1 odd day
- 2023 = Normal Year = 1 odd day
- 2024 = Leap Year = 2 odd days
- 2025 = Normal Year = 1 odd day
Total odd days:
1 + 1 + 1 + 2 + 1 = 6
Move 6 days forward from Friday:
- Saturday = 1
- Sunday = 2
- Monday = 3
- Tuesday = 4
- Wednesday = 5
- Thursday = 6
Therefore, 1 January 2026 was Thursday.
Conclusion
Calendar questions may seem difficult at first, but they become much easier once you understand the basic concepts. In this guide, we learned about years, leap years, odd days, month codes, and different Calendar Problems Tricks that are commonly used in competitive exams.
The key to mastering calendar questions is regular practice. Do not try to memorize every shortcut at once. First, understand the logic behind the concepts and then practice applying them to different types of questions. The more questions you solve, the faster and more accurate you will become.
Make it a habit to revise the important rules, month codes, and odd day calculations regularly. Even spending a few minutes each day practicing Calendar Problems Tricks can significantly improve your speed and confidence in exams.
With consistent revision and practice, calendar aptitude questions can become one of the easiest and highest-scoring topics in competitive exams.
Frequently Asked Questions (FAQs)
Q1. What is a leap year?
A: A leap year is a year that contains 366 days instead of 365 days. In a leap year, February has **29 days instead of 28 days.
Q2. How can I identify a leap year?
A: A year is a leap year if it is divisible by 4. However, century years must also be divisible by 400. For example, 2000 was a leap year, but 1900 was not.
Q3. What are odd days in calendar problems?
A: Odd days are the remaining days after dividing the total number of days by 7. They are used to determine the day of the week for a given date.
Q4. Why are month codes important in calendar questions?
A: Month codes help simplify calendar calculations by representing the cumulative odd days before a month begins. They allow you to find the day of the week more quickly.
Q5. How can I improve at solving calendar problems?
A: Start by understanding the basics such as leap years, odd days, and month codes. Then practice different types of calendar questions regularly and revise the important rules daily to improve your speed and accuracy.
