Calendar
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Solved Examples
Study MaterialSolved Examples – Calendar
Solved examples help students understand the practical application of calendar concepts in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, Defence, and various aptitude examinations.
Topics Covered in Solved Examples
- Odd Day Calculations
- Leap Year Problems
- Finding Day of a Date
- Reference Day Questions
- Repeated Calendar Problems
- Month and Year Code Questions
- Day Gain and Loss Concepts
- Advanced Calendar Aptitude Problems
Example 1: Odd Days in an Ordinary Year
Question: How many odd days are there in an ordinary year?
Solution:
An ordinary year has:
365 days
365 = 52 weeks + 1 day
Therefore:
Odd Days = 1
Example 2: Odd Days in a Leap Year
Question: How many odd days are there in a leap year?
Solution:
A leap year has:
366 days
366 = 52 weeks + 2 days
Therefore:
Odd Days = 2
Example 3: Identifying Leap Year
Question: Which of the following is a leap year: 1900, 2000, 2023, 2024?
Solution:
- 1900 → Not divisible by 400 → Not Leap Year
- 2000 → Divisible by 400 → Leap Year
- 2023 → Not divisible by 4 → Not Leap Year
- 2024 → Divisible by 4 → Leap Year
Therefore:
Leap Years = 2000 and 2024
Example 4: Finding Day After Certain Days
Question: If today is Monday, what day will it be after 45 days?
Solution:
45 ÷ 7 gives remainder:
= 3
Move 3 days forward from Monday:
- Tuesday → 1
- Wednesday → 2
- Thursday → 3
Therefore:
Required Day = Thursday
Example 5: Finding Day Before Certain Days
Question: If today is Friday, what day was it 20 days ago?
Solution:
20 ÷ 7 gives remainder:
= 6
Move 6 days backward from Friday:
- Thursday → 1
- Wednesday → 2
- Tuesday → 3
- Monday → 4
- Sunday → 5
- Saturday → 6
Therefore:
Required Day = Saturday
Example 6: Odd Days in 100 Years
Question: How many odd days are there in 100 years?
Solution:
Important fact:
100 years = 5 odd days
Therefore:
Odd Days = 5
Example 7: Finding Day of a Date
Question: What day was 15 August 1947?
Solution:
Known historical fact:
15 August 1947 was India's Independence Day.
It was:
Friday
Example 8: Repeated Calendar Problem
Question: After how many years does an ordinary year calendar repeat?
Solution:
Ordinary year calendar repeats after:
- 6 years
- 11 years
Therefore:
Answer = 6 or 11 years
Example 9: Leap Year Calendar Repetition
Question: After how many years does a leap year calendar repeat?
Solution:
Leap year calendar repeats after:
= 28 years
Therefore:
Answer = 28 years
Example 10: Counting Odd Days Quickly
Question: Find odd days in 800 days.
Solution:
800 ÷ 7 gives remainder:
= 2
Therefore:
Odd Days = 2
Example 11: Reference Day Problem
Question: If 1 January is Monday, what day will be 10 January?
Solution:
Difference:
= 10 − 1
= 9 days
9 ÷ 7 gives remainder:
= 2
Move 2 days ahead from Monday:
- Tuesday → 1
- Wednesday → 2
Therefore:
Required Day = Wednesday
Example 12: Century Leap Year Problem
Question: Is the year 2400 a leap year?
Solution:
2400 is divisible by 400.
Therefore:
2400 is a Leap Year
Example 13: Day Code Problem
Question: If odd days are 5, what is the corresponding day?
Solution:
Using day code table:
- 0 → Sunday
- 1 → Monday
- 2 → Tuesday
- 3 → Wednesday
- 4 → Thursday
- 5 → Friday
Therefore:
Required Day = Friday
Example 14: Important 400-Year Concept
Question: Why does calendar repeat after every 400 years?
Solution:
In 400 years:
Total odd days become multiples of 7.
Therefore:
Calendar repeats exactly after 400 years.
Answer:
Because total odd days become complete weeks.
Example 15: February Leap Year Exception
Question: If 10 January 2020 was Friday, what day was 10 January 2021?
Solution:
2020 is a leap year.
But January 10 does not cross February 29.
Therefore only 1 odd day is added.
Friday + 1 day:
= Saturday
Therefore:
Required Day = Saturday
Example 16: Month Day Counting
Question: How many days are there from 1 April to 1 May?
Solution:
April has:
= 30 days
Therefore:
Total Days = 30
Example 17: Day Calculation Using Odd Days
Question: If today is Sunday, what day will it be after 100 days?
Solution:
100 ÷ 7 gives remainder:
= 2
Move 2 days ahead from Sunday:
- Monday → 1
- Tuesday → 2
Therefore:
Required Day = Tuesday
Example 18: Advanced Calendar Problem
Question: How many leap years are there between 2001 and 2020?
Solution:
Leap years:
- 2004
- 2008
- 2012
- 2016
- 2020
Total:
= 5 leap years
Therefore:
Answer = 5
Important Exam Tips
- Memorize leap year rules carefully.
- Practice odd day calculations regularly.
- Use modulo 7 calculations.
- Remember leap year February exception.
- Use reference day techniques.
- Practice repeated calendar questions.
- Verify calculations carefully.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving calendar questions in competitive examinations.