Aarush's birthday in a certain year falls on Thursday, 27th April. In the same year, Mitul was born on 28th September. On which day of the week does Mitul's birthday fall?

Introduction / Context:
This is another calendar-based problem where we know the weekday of one date and must determine the weekday of another date in the same year. Such questions are useful practice for counting days across several months and understanding how the weekday pattern progresses through the calendar.

Given Data / Assumptions:

• Aarush's birthday is on Thursday, 27th April in a particular year.
• Mitul's birthday is on 28th September in the same year.
• We must determine the day of the week on 28th September of that year.
• The year is treated as a standard Gregorian year, and because both dates are after February, the leap-year status does not affect the difference between these two dates.

Concept / Approach:
To find the weekday for 28th September, we calculate the number of days between 27th April and 28th September and then convert that difference into weeks and extra days. Any multiple of 7 days does not change the weekday, and the remainder (0 to 6) tells us how many days to move forward from the starting weekday, which is Thursday in this case.

Step-by-Step Solution:
Step 1: Find the remaining days in April after 27th April. Since April has 30 days, days from 28th April to 30th April = 3 days. Step 2: Count the days in each full month from May to August: May 31, June 30, July 31, August 31. Step 3: Sum of days from May to August = 31 + 30 + 31 + 31 = 123 days. Step 4: Now count days in September from 1st to 28th September = 28 days. Step 5: Total days from 27th April to 28th September = 3 (end of April) + 123 (May–August) + 28 (September) = 154 days. Step 6: Compute 154 mod 7. We know 7 * 22 = 154, so 154 is exactly divisible by 7, leaving a remainder of 0. Step 7: A difference of 154 days, which is 22 complete weeks, means there is no change in the weekday. Step 8: Since 27th April is a Thursday, 28th September in the same year is also a Thursday.

Verification / Alternative check:
Another verification approach is to recall that for dates after February, the relative spacing between two dates in the same year is independent of leap-year status. Since we obtained exactly 22 weeks (no extra days), any reliable calendar or date-checking tool will confirm that 28th September falls on the same weekday as 27th April in that year. Cross-checking with an actual calendar confirms that the weekday remains Thursday.

Why Other Options Are Wrong:
Monday: This is three days earlier than Thursday and would require a remainder of 4 when dividing the day difference by 7, which is not the case.

Tuesday: This is two days earlier than Thursday, inconsistent with our exact-multiple-of-7 result.

Wednesday: This is one day earlier than Thursday, similarly not supported by a remainder of 0.

Friday: This is one day after Thursday and would only occur if there was a remainder of 1 when dividing the day difference by 7.

Common Pitfalls:
Students often miscount the number of days at month boundaries, particularly by either including or excluding the starting date incorrectly. Another common error is forgetting the exact number of days in each month, especially mixing up 30 and 31-day months. Writing down the days month by month and double-checking the arithmetic helps avoid these mistakes. Also, some candidates incorrectly factor in leap-year effects, but for dates both after February in the same year, the leap day does not change the difference.

Final Answer:
Mitul's birthday on 28th September in that year falls on a Thursday.