Arnav celebrates his birthday on Tuesday 14 March in a particular year. In the same year Pranay celebrates his birthday on 13 September. On which day of the week does Pranay's birthday fall?

Introduction / Context:
Here again we have a weekday calculation within the same year. The weekday of an earlier date is known and that of a later date must be deduced. Questions of this style are common in calendar topics, building confidence with day counting, month lengths and odd day concepts, which together form the backbone of many date based reasoning problems.

Given Data / Assumptions:

• Arnav has his birthday on Tuesday 14 March in a given year.
• Pranay has his birthday on 13 September in the same year.
• We must find the weekday for 13 September.
• Leap year issues do not affect the difference because both dates fall after February.

Concept / Approach:
The strategy is to find how many days lie between the two birthdays and then compute the remainder when that number is divided by 7. The remainder indicates how many days ahead in the weekly cycle we move from Tuesday to reach the weekday of the second date. This remainder is often called the number of odd days.

Step-by-Step Solution:
Step 1: Count remaining days in March after 14 March. March has 31 days, so remaining days are 31 - 14 = 17.Step 2: Add full months from April to August. April has 30 days, May 31, June 30, July 31 and August 31, for a total of 30 + 31 + 30 + 31 + 31 = 153 days.Step 3: Add days in September up to 13 September, which gives 13 days.Step 4: Total days between the birthdays equals 17 + 153 + 13 = 183 days.Step 5: Compute 183 modulo 7. Since 7 * 26 = 182, the remainder is 1. Thus there is exactly 1 odd day between the two dates. Moving forward 1 day from Tuesday lands on Wednesday. Hence Pranay's birthday falls on Wednesday.
Verification / Alternative check:
If we view 183 as 182 plus 1, then the 182 days correspond to 26 full weeks that do not alter the weekday. Only the extra 1 day shifts the weekday forward by one step. Starting from Tuesday and moving one step ahead reaches Wednesday. Both the modulo view and the week based view give the same conclusion.

Why Other Options Are Wrong:
Monday would require moving backward from Tuesday, but the calculated remainder is positive, not negative.Tuesday would be correct only if the total number of days between the birthdays were a multiple of 7, which 183 is not.Thursday would correspond to a shift of 2 days from Tuesday, conflicting with the remainder of 1.
Common Pitfalls:
Students may forget that March has 31 days or miscalculate one of the month lengths. Others mistakenly treat 183 as exactly divisible by 7, which it is not. Careful writing of partial sums and a deliberate modulo 7 operation ensure an error free solution for this and similar questions.

Final Answer:
Pranay's birthday on 13 September falls on Wednesday.