Question

If \( 15^{\text{th}} \) August, 2023 was on Tuesday, then on which day of the week would the Independence Day be celebrated in the year 2040?

• A. Tuesday
• B. Wednesday
• C. Thursday
• D. Friday

Hint:

For the same date in different years, use the shortcut: \[ \text{Odd Days} = (\text{Year Difference} + \text{Number of Leap Years}) \pmod 7 \] Then move forward that many days from the given weekday.

Answer 1

The Correct Option is B

Concept: To determine the day of the week for a future date, we calculate the total number of odd days between the two dates.
• A normal year contributes \(1\) odd day.
• A leap year contributes \(2\) odd days.
• A leap year occurs when the year is divisible by \(4\) (for non-centurial years).

Step 1: Calculate the number of years between the two dates. \[ 2040 - 2023 = 17 \text{ years} \] Thus, the period from \(15^{\text{th}}\) August 2023 to \(15^{\text{th}}\) August 2040 spans \(17\) years.

Step 2: Count the leap years in this interval. The leap years occurring before \(15^{\text{th}}\) August 2040 are: \[ 2024,\; 2028,\; 2032,\; 2036,\; 2040 \] Hence, \[ \text{Number of leap years} = 5 \]

Step 3: Calculate the total odd days. Every year contributes one odd day, and each leap year contributes one additional odd day. \[ \text{Total Odd Days} = 17 + 5 = 22 \] Now, \[ 22 \mod 7 = 1 \] Therefore, there is a net advancement of \(1\) day.

Step 4: Determine the required day. Given: \[ 15^{\text{th}} \text{ August, 2023} = \text{Tuesday} \] Adding \(1\) day: \[ \text{Tuesday} + 1 = \text{Wednesday} \] Hence, Independence Day in the year \(2040\) will be celebrated on Wednesday.