Dhruv's birthday in a particular year falls on Sunday, 28th May. In the same year, Sahil was born on 19th October. On which day of the week does Sahil's birthday fall in that year?

Introduction / Context:
This question connects two birthdays within the same calendar year. You are given the day of the week for Dhruv's birthday and must determine the weekday for Sahil's birthday. Solving this requires counting the number of days between two dates spread across several months and then converting that interval into a weekday shift.

Given Data / Assumptions:

• Dhruv's birthday: Sunday, 28th May (in some year).
• Sahil's birthday: 19th October of the same year.
• Standard month lengths:
  • May: 31 days
  • June: 30 days
  • July: 31 days
  • August: 31 days
  • September: 30 days
  • October: 31 days
• Since both dates are after February, leap year vs non-leap year does not affect their relative difference.

Concept / Approach:
We find the total number of days from 28th May to 19th October, then take this total modulo 7 to determine how many days forward we move from Dhruv's birthday. The resulting shift in days gives the weekday for Sahil's birthday.

Step-by-Step Solution:
Step 1: Days remaining in May after 28th May: 31 - 28 = 3 days (29th, 30th, 31st). Step 2: Full months between June and September: June: 30 days, July: 31 days, August: 31 days, September: 30 days. Step 3: Total days from June to September inclusive = 30 + 31 + 31 + 30 = 122 days. Step 4: Days in October up to 19th October = 19 days. Step 5: Total days between 28th May and 19th October = 3 (end of May) + 122 (June to September) + 19 (October) = 144 days. Step 6: Compute 144 mod 7. Since 7 * 20 = 140, remainder is 144 - 140 = 4. Step 7: A remainder of 4 means we move 4 days forward from Sunday. Step 8: Starting from Sunday: Monday (1), Tuesday (2), Wednesday (3), Thursday (4). Step 9: So Sahil's birthday on 19th October falls on a Thursday.

Verification / Alternative check:
You can think of 144 days as 20 full weeks (140 days) plus 4 extra days. The 20 full weeks bring the weekday back to Sunday, and the extra 4 days shift Sunday forward to Thursday. Because we have used standard month lengths and both dates are after February, the calculation is independent of the specific year and thus robust.

Why Other Options Are Wrong:
Saturday would require a shift of 6 days from Sunday, Wednesday a shift of 3 days and Sunday a shift of 0 days. Monday would imply only a 1-day shift. None of these match the 4-day shift resulting from 144 days, so they are inconsistent with the actual day difference between the two birthdays.

Common Pitfalls:
Miscounting days in one or more months is a common error, especially mixing up 30-day and 31-day months. Another mistake is forgetting to include the correct number of days in the starting and ending months. Always list the months and their lengths explicitly when the interval spans many months, and then reduce the final count modulo 7.

Final Answer:
Sahil's birthday in that year falls on Thursday.