# 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**.