What will be the day of the week 15th August 2010?a)Sundayb)Mondayc)Tu...
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days ≡ 4 odd days.
Jan. Feb. March April Mayb June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
∴ 227 days = (32 weeks + 3 days) ≡ 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 ≡ 0 odd days.
Given day is Sunday
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What will be the day of the week 15th August 2010?a)Sundayb)Mondayc)Tu...
**Explanation:**
To determine the day of the week for a given date, we can use the concept of the Gregorian calendar and some basic calculations.
**Step 1: Determining the Reference Day**
- To find the day of the week for a specific date, we need to determine a reference day. In this case, we can choose a known day and its corresponding date that falls within the same year as the given date. Let's choose the reference day as January 1, 2010, which was a Friday.
**Step 2: Counting the Number of Days**
- The next step is to count the number of days between the reference day and the given date. For this, we need to consider both the number of days within the same year and the number of days in the intervening years.
- From January 1, 2010, to August 15, 2010, there are 226 days.
- Additionally, we need to consider the number of days in the intervening years (2011-2019) between the reference year and the given year. There are 9 years, and each year has 365 days, so the total number of intervening days is 9 * 365 = 3285.
- Therefore, the total number of days between the reference day and August 15, 2010, is 226 + 3285 = 3511.
**Step 3: Determining the Day of the Week**
- Now, we need to find the remainder when the total number of days is divided by 7. This remainder will give us the day of the week.
- 3511 divided by 7 equals 501 remainder 4.
- Since the reference day was Friday (which corresponds to 0), we can count 4 days forward to determine the day of the week for August 15, 2010.
- Friday (0) -> Saturday (1) -> Sunday (2) -> Monday (3) -> **Tuesday (4)**.
Therefore, the day of the week for August 15, 2010, was **Tuesday**.
What will be the day of the week 15th August 2010?a)Sundayb)Mondayc)Tu...
Just see the calendar and find out