Q. Which date of June 2099 among the following is Sunday?
a. 4
b. 5
c. 6
d. 7
Correct Answer: d. 7
Question from UPSC Prelims 2022 CSAT Paper
Explanation :
June 2099 – Sunday
Prelims 2022 – 5-JUN-2022 Sunday.
First, calculate the number of years between 2022 and 2099, which is 2099 – 2022 = 77 years.
Determining Number of Leap Years
Next, determine the number of leap years in this period. Leap years are typically every 4 years, but we must exclude centuries that are not divisible by 400. The years from 2022 to 2099 include the following leap years: 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076, 2080, 2084, 2088, 2092, 2096. That’s a total of 19 leap years.
Calculating Total Number of Odd Days
Each normal year contributes 1 odd day (365 days = 52 weeks + 1 day), and each leap year contributes 2 odd days (366 days = 52 weeks + 2 days).
So, the total number of odd days in 77 years is:
- Odd days from normal years = 58 normal years × 1 odd day = 58 odd days
- Odd days from leap years = 19 leap years × 2 odd days = 38 odd days
- Total odd days = 58 + 38 = 96 odd days
Determining the Day of the Week
Since each week has 7 days, we find the remainder of 96 divided by 7 to get the number of odd days:
96 mod 7 = 5 odd days
Since June 5, 2022, was a Sunday, adding 5 odd days means:
Sunday + 5 days = Friday
Thus, June 5, 2099, will be a Friday.
