Measurement / Mensuration - The Calendar
Introduction
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. It helps us track time in terms of days, weeks, months, and years.
Explanation Step by Step
Key units of time in a calendar:
- 1 Day = 24 Hours
- 1 Week = 7 Days
- 1 Year = 12 Months (52 Weeks)
- Normal Year = 365 Days
- Leap Year = 366 Days (February has 29 days)
Gregorian and Indian National Months
| No. | Gregorian Month | Days | Indian Month | Days |
|---|---|---|---|---|
| 1 | January | 31 | Chaitra | 30/31 |
| 2 | February | 28/29 | Vaishakh | 31 |
| 3 | March | 31 | Jyeshtha | 31 |
| 4 | April | 30 | Ashadha | 31 |
| 5 | May | 31 | Shravan | 31 |
| 6 | June | 30 | Bhadrapad | 31 |
| 7 | July | 31 | Ashwin | 30 |
| 8 | August | 31 | Kartik | 30 |
| 9 | September | 30 | Agrahayana | 30 |
| 10 | October | 31 | Pausha | 30 |
| 11 | November | 30 | Magha | 30 |
| 12 | December | 31 | Phalguna | 30 |
Sub-topics
The Calendar and Leap Years
A year divisible by 4 is a leap year. For century years (like 1900, 2000), they must be divisible by 400 to be a leap year. Example: 2000 was a leap year, but 2100 will not be.
Examples
Example 1: Converting Years to Months
How many months are there in 3 years?
Calculation: 3 years × 12 months/year
36 months.
Tricks and Shortcuts
- The same day of the week repeats every 7 days.
- In a 31-day month, dates 1, 2, and 3 occur 5 times.
- If a year is not a leap year, it starts and ends on the same day of the week.
- Independence Day, Children's Day, and Teachers' Day fall on the same day of the week in a given year.
Common Mistakes
- Confusing "from date" and "after date". Counting "from the 10th" includes the 10th, while "after the 10th" starts from the 11th.
- Assuming all years divisible by 4 are leap years (century years need 400).
Practice Questions
Easy Questions
- How many days are there in a leap year?
- Which month comes after August?
- How many weeks make a year?
Medium Questions
- If today is Friday, what day will it be after 14 days?
- Identify if 1996 is a leap year.
- How many days are there between Monday and Friday?
Hard Questions
- If Jan 1st, 2016 (Leap Year) was a Friday, what day was Jan 1st, 2017?
- A boy traveled from the 15th of March to the 22nd of March. For how many days did he travel?
- In a month of 30 days, if the 1st is a Sunday, which days will appear 5 times?
Revision Summary
Understanding the calendar requires knowing the number of days in each month and the rules of leap years. Remember the 7-day repetition rule to solve date-related problems quickly.
If February 1st is a Monday (normal year), then what day is February 28th?
A
Sunday
B
Monday
C
Tuesday
D
Wednesday
If April 1st is a Saturday, what day is April 15th?
A
Friday
B
Saturday
C
Sunday
D
Monday