Divyansh's birthday in a certain year falls on Sunday, 16th July. In the same year, Shaan was born on 1st August. In that year, on which day of the week does Shaan's birthday fall?

Introduction / Context:
This calendar problem asks you to determine the weekday of one birthday given the weekday of another birthday in the same year. Both dates occur after February, so leap year effects on February do not alter the difference. The main skills tested are counting days between calendar dates and then converting that difference into a shift in weekdays.

Given Data / Assumptions:

• Divyansh's birthday: Sunday, 16th July (same year as Shaan).
• Shaan's birthday: 1st August of the same year.
• Month lengths: July has 31 days; August has 31 days.
• We use the standard Gregorian calendar.

Concept / Approach:
To find the weekday difference, we count the number of days from 16th July to 1st August and then reduce that number modulo 7. A positive result tells us how many days forward in the week we must move from Sunday. Since both dates are in the same year and after February, we do not need to worry about leap years changing the relative difference between these two dates.

Step-by-Step Solution:
Step 1: Identify how many days remain in July after 16th July. Step 2: July has 31 days, so the days remaining after 16th are: 17th to 31st inclusive. Step 3: Count these days: 31 - 16 = 15 days remaining in July. Step 4: From 16th July to 1st August, we move 15 days to get to 31st July and then 1 more day to get to 1st August. Step 5: Total number of days between 16th July and 1st August = 15 + 1 = 16 days. Step 6: Compute 16 mod 7. Since 14 is a multiple of 7, 16 = 14 + 2, so 16 mod 7 = 2. Step 7: A shift of 2 days forward from Sunday gives: Monday (1 day ahead), Tuesday (2 days ahead). Step 8: Therefore, Shaan's birthday on 1st August falls on a Tuesday.

Verification / Alternative check:
You can also see 16 days as two full weeks (14 days) plus 2 extra days. Two full weeks bring the weekday back to Sunday, and the extra 2 days move Sunday to Tuesday. Hence the answer is consistent regardless of the exact year chosen, as long as we preserve the usual month lengths.

Why Other Options Are Wrong:
Monday would correspond to a shift of 1 day, which would require a 15-day gap, not the 16 days actually present. Wednesday would be 3 days ahead, and Sunday would correspond to a multiple of exactly 7 days with no remainder. Thursday would imply a 4-day shift. Only a 2-day shift matches the correct count of 16 days.

Common Pitfalls:
Students sometimes miscount days by including the starting day or excluding the ending day incorrectly. A robust method is to count how many days you must move forward from the first date to land on the second date, not counting the starting day itself. Also, always remember to reduce the total count modulo 7 instead of trying to step through each day individually.

Final Answer:
Shaan's birthday in that year falls on Tuesday.