Comprehensive study of odd days in calendars, covering calculations for months, years, and centuries, essential for CBSE Class 11 Applied Mathematics students to master chronological reasoning.
An 'odd day' is the remainder obtained when the total number of days in a given period is divided by 7. Since a week consists of 7 days, the remaining days represent the offset beyond complete weeks. This is a fundamental concept for determining days of the week for specific dates.
• A leap year has 366 days.
• Divide 366 by 7: 366 = (52 * 7) + 2.
• The remainder is 2.
Answer: There are 2 odd days in a leap year.
The number of odd days in a month depends on the total number of days in that specific month. For months with 31 days, 31 mod 7 = 3 odd days. For months with 30 days, 30 mod 7 = 2 odd days.
• A non-leap year February has 28 days.
• Divide 28 by 7: 28 = (4 * 7) + 0.
• The remainder is 0.
Answer: There are 0 odd days in February of a non-leap year.
A century consists of 100 years. It contains 76 ordinary years and 24 leap years (since every 4th year is a leap year, 100/4 = 25, but the 100th year is not a leap year unless divisible by 400). Total days = (76 * 365) + (24 * 366) = 36524 days. Dividing 36524 by 7 leaves a remainder of 5.
• Number of odd days in 100 years = 5.
• Number of odd days in 200 years = (5 * 2) = 10.
• Divide 10 by 7: 10 mod 7 = 3.
Answer: There are 3 odd days in 200 years.