Faiyaz celebrates his birthday on Wednesday 12 April in a certain year. In the same year Shray celebrates his birthday on 2 October. On which day of the week does Shray's birthday fall?

Introduction / Context:
This calendar problem requires calculating the weekday of a date later in the year when the weekday of an earlier date is known. Mastery of such questions comes from comfort with counting days across months and using odd days to capture the net shift in weekday. These ideas are widely tested in competitive exams under the calendar or time and date topic.

Given Data / Assumptions:

• Faiyaz has his birthday on Wednesday 12 April in a particular year.
• Shray has his birthday on 2 October in the same year.
• We must find the weekday on which 2 October falls.
• Whether the year is leap or non leap does not affect the calculation because both dates lie after February.

Concept / Approach:
We will compute the number of days between 12 April and 2 October. Dividing this count by 7 gives the number of odd days, which tells us how far forward we need to move from Wednesday to reach the weekday of 2 October. Complete weeks consisting of 7 days do not change the weekday, so only the remainder matters.

Step-by-Step Solution:
Step 1: Compute remaining days in April after 12 April. Since April has 30 days, remaining days are 30 - 12 = 18.Step 2: Add days in full months from May to September. May has 31 days, June 30, July 31, August 31 and September 30. The total is 31 + 30 + 31 + 31 + 30 = 153 days.Step 3: Add days in October up to 2 October, which contributes 2 days.Step 4: Total days between the two birthdays equal 18 + 153 + 2 = 173 days.Step 5: Compute 173 modulo 7. Since 7 * 24 = 168, the remainder is 5. So there are 5 odd days between the two dates. Starting from Wednesday and moving forward 5 days gives Thursday (1), Friday (2), Saturday (3), Sunday (4) and Monday (5). Therefore Shray's birthday falls on Monday.
Verification / Alternative check:
We can see 173 as 168 plus 5. The 168 days correspond to 24 full weeks, which bring us back to Wednesday. The extra 5 days shift us forwards by 5 positions in the weekly cycle, landing on Monday. This alternate reasoning matches the modulo calculation and confirms the result.

Why Other Options Are Wrong:
Saturday corresponds to a shift of 3 days from Wednesday, which is not equal to the calculated shift of 5.Wednesday would require no net shift in weekday, which would happen only if the total days were exactly divisible by 7.Sunday is 4 days ahead of Wednesday, again inconsistent with the remainder of 5.
Common Pitfalls:
Common errors include miscounting the days in April or forgetting that June and September have only 30 days. Some students also misapply modulo arithmetic and interpret the remainder incorrectly on the weekday circle. Writing the month wise breakdown clearly and then mapping the remainder to a forward move from Wednesday keeps the reasoning transparent and reliable.

Final Answer:
Shray's birthday on 2 October falls on Monday.