Hansh's birthday in a certain year falls on Monday, 5th June. In the same year, Tushar was born on 11th December. On which day of the week does Tushar's birthday fall in that year?

Introduction / Context:
This calendar problem provides the weekday for one birthday and asks you to determine the weekday for another birthday in the same year. You need to count how many days separate the two dates, then convert this into a weekday shift using modulo 7 arithmetic. Because both dates are well after February, leap-year differences do not affect their relative spacing.

Given Data / Assumptions:

• Hansh's birthday: Monday, 5th June.
• Tushar's birthday: 11th December of the same year.
• Standard month lengths:
  • June: 30 days
  • July: 31 days
  • August: 31 days
  • September: 30 days
  • October: 31 days
  • November: 30 days
  • December: 31 days
• We consider a usual Gregorian year.

Concept / Approach:
We compute the total number of days between 5th June and 11th December, then reduce this total modulo 7. This gives the number of days to move forward from Monday (the weekday of 5th June) to reach the weekday of 11th December in the same year.

Step-by-Step Solution:
Step 1: Days remaining in June after 5th June: 30 - 5 = 25 days (6th to 30th). Step 2: Full months from July to November: July: 31 days, August: 31 days, September: 30 days, October: 31 days, November: 30 days. Step 3: Sum for July to November = 31 + 31 + 30 + 31 + 30 = 153 days. Step 4: Days in December up to 11th December = 11 days. Step 5: Total days between 5th June and 11th December = 25 (June) + 153 (July to November) + 11 (December) = 189 days. Step 6: Compute 189 mod 7. Since 7 * 27 = 189 exactly, the remainder is 0. Step 7: A remainder of 0 means the total time spans an exact number of weeks, so the weekday remains unchanged. Step 8: Therefore, 11th December falls on the same weekday as 5th June, which is Monday.

Verification / Alternative check:
Seeing 189 as 27 full weeks (27 * 7) makes it clear that we have only complete weeks between the two dates, with no extra days to shift the weekday. If 5th June is a Monday, then every date exactly 7 days away in either direction is also a Monday, and after 27 such weeks we again land on a Monday. This reasoning confirms the result independently of any specific year choice.

Why Other Options Are Wrong:
Sunday, Wednesday, Tuesday or Friday would all require a non-zero remainder when dividing the day difference by 7. Since our calculation shows a remainder of zero, the weekday must remain the same. Any option different from Monday contradicts the fact that 189 days form an exact multiple of weeks.

Common Pitfalls:
Miscounting the number of days in one of the months, especially mixing 30-day and 31-day months, can lead to a day difference that is not a multiple of 7 and hence a wrong weekday. Writing down each month's length and adding carefully, followed by a modulo 7 step, is a reliable strategy for avoiding these errors.

Final Answer:
Tushar's birthday in that year falls on Monday.