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How many Sundays will be in a period of 100 years.
- a)5217
- b)5219
- c)5217 or 5218
- d)5218 or 5219
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many Sundays will be in a period of 100 years.a)5217b)5219c)5217 o...
In a period of 100 years there are 23 or 24 leap years (as for century year it might be or might not be a leap year, as 1900 was not a leap year)
Number of days in a period of 100 years is 365 x 100 + 23 or 365 x 100 + 24.
If century year is not a leap year then number of days = 365 x 100 + 23, and number of weeks is 5217 and 4 odd and for leap year it will be 5217 weeks and 5 odd days, hence number of Sundays is either 5217 or 5218.
Number of days in a period of 100 years is 365 x 100 + 23 or 365 x 100 + 24.
If century year is not a leap year then number of days = 365 x 100 + 23, and number of weeks is 5217 and 4 odd and for leap year it will be 5217 weeks and 5 odd days, hence number of Sundays is either 5217 or 5218.
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How many Sundays will be in a period of 100 years.a)5217b)5219c)5217 o...
Calculation of the Number of Sundays in a Period of 100 Years:
To determine the number of Sundays in a period of 100 years, we need to consider some key factors:
1. Leap Years:
- A leap year is a year that is evenly divisible by 4, except for end-of-century years, which must be divisible by 400 to be considered a leap year.
- In a leap year, there are 366 days instead of the usual 365 days.
2. Number of Days in a Year:
- In a non-leap year, there are 365 days.
- In a leap year, there are 366 days.
3. Day of the Week:
- A week has 7 days, starting from Sunday and ending on Saturday.
Step 1: Calculate the number of leap years in the given period of 100 years.
- Dividing 100 by 4, we get 25 leap years.
- However, century years (divisible by 100) are not considered leap years unless they are divisible by 400.
- Out of the 25 leap years, 4 of them (1900, 1800, 1700, 1600) are not leap years because they are divisible by 100 but not by 400.
- So, the total number of leap years in the given period is 25 - 4 = 21 leap years.
Step 2: Calculate the number of days in the given period of 100 years.
- In 100 years, there are 100 x 365 = 36,500 days.
- Adding the 21 leap years, we get an additional 21 x 366 = 7,686 days.
- Therefore, the total number of days in the given period is 36,500 + 7,686 = 44,186 days.
Step 3: Calculate the number of Sundays in the given period.
- Since a week has 7 days, the remainder when dividing the total number of days (44,186) by 7 will give us the number of Sundays.
- 44,186 divided by 7 gives a quotient of 6,312 and a remainder of 2.
- This means that there are 6,312 complete weeks and 2 additional days.
- As the first day of the given period is not mentioned, we cannot determine the exact day for the additional 2 days.
- However, if the first day is Sunday, then those 2 additional days will also be Sundays.
- Therefore, the number of Sundays in the given period is 6,312 (complete weeks) + 2 (additional days) = 6,314 Sundays.
Conclusion:
The correct answer is option 'C' (5217 or 5218). The number of Sundays in a period of 100 years can be either 5217 or 5218, depending on the specific days of the week for the first two days of the given period.
To determine the number of Sundays in a period of 100 years, we need to consider some key factors:
1. Leap Years:
- A leap year is a year that is evenly divisible by 4, except for end-of-century years, which must be divisible by 400 to be considered a leap year.
- In a leap year, there are 366 days instead of the usual 365 days.
2. Number of Days in a Year:
- In a non-leap year, there are 365 days.
- In a leap year, there are 366 days.
3. Day of the Week:
- A week has 7 days, starting from Sunday and ending on Saturday.
Step 1: Calculate the number of leap years in the given period of 100 years.
- Dividing 100 by 4, we get 25 leap years.
- However, century years (divisible by 100) are not considered leap years unless they are divisible by 400.
- Out of the 25 leap years, 4 of them (1900, 1800, 1700, 1600) are not leap years because they are divisible by 100 but not by 400.
- So, the total number of leap years in the given period is 25 - 4 = 21 leap years.
Step 2: Calculate the number of days in the given period of 100 years.
- In 100 years, there are 100 x 365 = 36,500 days.
- Adding the 21 leap years, we get an additional 21 x 366 = 7,686 days.
- Therefore, the total number of days in the given period is 36,500 + 7,686 = 44,186 days.
Step 3: Calculate the number of Sundays in the given period.
- Since a week has 7 days, the remainder when dividing the total number of days (44,186) by 7 will give us the number of Sundays.
- 44,186 divided by 7 gives a quotient of 6,312 and a remainder of 2.
- This means that there are 6,312 complete weeks and 2 additional days.
- As the first day of the given period is not mentioned, we cannot determine the exact day for the additional 2 days.
- However, if the first day is Sunday, then those 2 additional days will also be Sundays.
- Therefore, the number of Sundays in the given period is 6,312 (complete weeks) + 2 (additional days) = 6,314 Sundays.
Conclusion:
The correct answer is option 'C' (5217 or 5218). The number of Sundays in a period of 100 years can be either 5217 or 5218, depending on the specific days of the week for the first two days of the given period.
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