Faiyaz's birthday in a certain year falls on Wednesday, 12th April. In the same year, Shray was born on 2nd October. On which day of the week does Shray's birthday fall in that year?

Introduction / Context:
This is a calendar-based problem involving two birthdays in the same year. You know the weekday of Faiyaz's birthday and must find the weekday of Shray's birthday. Because the two dates (12th April and 2nd October) are separated by several months, we need to count the total days between them and then convert that total into a weekday shift using modulo 7.

Given Data / Assumptions:

• Faiyaz's birthday: Wednesday, 12th April (in some year).
• Shray's birthday: 2nd October of the same year.
• Standard month lengths:
  • April: 30 days
  • May: 31 days
  • June: 30 days
  • July: 31 days
  • August: 31 days
  • September: 30 days
  • October: 31 days
• Both birthdays are after February, so leap year vs non-leap year does not change their relative difference.

Concept / Approach:
We first calculate how many days lie between 12th April and 2nd October. Then we take that number modulo 7 to determine how many days forward we move from Wednesday. The weekday shift we obtain will be the weekday of Shray's birthday.

Step-by-Step Solution:
Step 1: Days remaining in April after 12th April: 30 - 12 = 18 days (13th to 30th). Step 2: Full months from May to September: May: 31 days, June: 30 days, July: 31 days, August: 31 days, September: 30 days. Step 3: Total days for May to September inclusive = 31 + 30 + 31 + 31 + 30 = 153 days. Step 4: Days in October up to 2nd October = 2 days. Step 5: Total days between 12th April and 2nd October = 18 (April) + 153 (May to September) + 2 (October) = 173 days. Step 6: Compute 173 mod 7. Since 7 * 24 = 168, remainder is 173 - 168 = 5. Step 7: A remainder of 5 means we move 5 days forward from Wednesday. Step 8: Starting from Wednesday: Thursday (1), Friday (2), Saturday (3), Sunday (4), Monday (5). Step 9: Hence, Shray's birthday on 2nd October falls on a Monday.

Verification / Alternative check:
Interpreting 173 as 24 full weeks (168 days) plus 5 extra days shows that only the 5 extra days affect the weekday. Full weeks bring you back to the same weekday. From Wednesday, five steps forward lead to Monday, confirming the result regardless of the specific year.

Why Other Options Are Wrong:
Saturday, Wednesday, Sunday or Friday correspond to 3, 0, 4 or 2 days of shift from Wednesday respectively. None of these match the required 5-day forward shift produced by 173 days. Therefore, those options cannot represent the correct weekday for Shray's birthday.

Common Pitfalls:
Miscounting days in one of the months, especially in April or around the October boundary, can change the day difference and thus the final weekday. Students also sometimes forget to reduce the total by modulo 7 and instead attempt to track each day manually. A structured month-by-month count followed by modulo 7 arithmetic keeps the reasoning clean and accurate.

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