Aarush birthday in a given year falls on Thursday, 27 April. In that same year, Mitul was born on 28 September. On which day of the week will Mitul birthday fall?

Introduction / Context:
This is another within year weekday calculation. Knowing that 27 April is a Thursday, we must work out the weekday on 28 September of the same year. Such questions require accurate counting of days over several months and then using modular arithmetic with seven day weeks to determine how far the weekday has advanced.

Given Data / Assumptions:
- Aarush birthday is on Thursday, 27 April. - Mitul birthday is on 28 September of the same year. - We treat the year as a typical non leap year. - Month lengths: April 30, May 31, June 30, July 31, August 31, September 30.

Concept / Approach:
The key is to calculate the number of days from 27 April to 28 September and then find this count modulo 7. Every complete group of 7 days simply cycles through a full week, so only the remainder affects the weekday. Once we find how many days beyond full weeks have passed, we add that many steps to Thursday to obtain the weekday for 28 September.

Step-by-Step Solution:
Step 1: Count remaining days in April after 27 April. The month has 30 days, so after the 27th there are 3 days (28, 29, 30). Step 2: Days in May = 31 days. Step 3: Days in June = 30 days. Step 4: Days in July = 31 days. Step 5: Days in August = 31 days. Step 6: Days in September up to 28 September from 1 September = 28 days. Step 7: Total days from 28 April to 28 September inclusive of 28 September = 3 + 31 + 30 + 31 + 31 + 28 = 154 days. Step 8: The number of days between 27 April and 28 September is 154 days. Step 9: Compute 154 mod 7. Since 7 * 22 = 154, the remainder is 0. Step 10: A remainder of 0 means that 28 September falls on the same weekday as 27 April. Step 11: Therefore 28 September is also a Thursday.

Verification / Alternative check:
We can think in terms of week blocks. Because 154 is exactly 22 weeks, there are 22 complete cycles of 7 days between 27 April and 28 September. Completing any whole number of weeks moves the calendar back to the same weekday. Thus, without checking every intermediate month again, we know that the weekday repeats, confirming that 28 September is Thursday when 27 April is Thursday in the same year.

Why Other Options Are Wrong:
- Monday, Tuesday, Wednesday, and Friday would correspond to remainders of 4, 5, 6, or 1 if we started from Thursday, but the actual remainder is 0. - Any answer other than Thursday would break the exact multiple of 7 days that separates the two dates.

Common Pitfalls:
Miscounting the days in the months or including or excluding the starting date incorrectly can easily lead to wrong remainders. Another frequent error is forgetting to convert the final total into a remainder modulo 7 and instead thinking that a large total automatically shifts the weekday significantly. Always reduce the total days modulo 7 and ensure the month lengths are correctly used for April, June, and other months with 30 days.

Final Answer:
Mitul birthday on 28 September of that year will fall on Thursday.