Arnav birthday is on Tuesday 14th March in a particular year. In the same year, on which day of the week will Pranay birthday fall if Pranay was born on 13th September?

Introduction / Context:
This calendar based reasoning question provides the day of the week for one date and asks you to determine the day for another date in the same year. Arnav birthday is on Tuesday 14th March, and you must find the weekday for 13th September of the same year, which is Pranay birthday. The problem tests your ability to count days across months and use modular arithmetic to track day of week shifts.

Given Data / Assumptions:

• Arnav birthday is Tuesday 14th March.
• Pranay birthday is 13th September of the same year.
• The year is not specified, but we only need the relative day, not the actual calendar year.
• Month lengths are taken as usual: March has 31 days, April 30, May 31, June 30, July 31, August 31 and September 30.
• We assume a standard Gregorian calendar and Arnav date as reference.

Concept / Approach:
The day of the week advances by one for each day that passes, wrapping around every seven days. To find the day for 13th September, compute the number of days between 14th March and 13th September, then take that number modulo 7. A remainder of 0 means the same day, 1 means one day later, and so on. Because February is before March, the leap year issue does not affect the count between these two dates.

Step-by-Step Solution:
Step 1: Count the days remaining in March after 14th March. March has 31 days, so there are 31 - 14 = 17 days from 15th March to 31st March.Step 2: Add the days in the full months between March and September. April has 30 days, May 31, June 30, July 31 and August 31.Step 3: For September, we count from 1st September up to 13th September, which is 13 days.Step 4: Sum all these days: 17 (rest of March) + 30 (April) + 31 (May) + 30 (June) + 31 (July) + 31 (August) + 13 (September).Step 5: Compute the total: 17 + 30 = 47, 47 + 31 = 78, 78 + 30 = 108, 108 + 31 = 139, 139 + 31 = 170, 170 + 13 = 183 days.Step 6: Find 183 modulo 7. Since 7 * 26 = 182, we get a remainder of 1.Step 7: A remainder of 1 means that 13th September is one day after the day on 14th March. Since 14th March is Tuesday, one day later is Wednesday.

Verification / Alternative check:
Another way to think about it is to note that 28 days is exactly 4 weeks, so contributes zero net shift in day of week. We can try to adjust the 183 days to the nearest multiple of 28 or 7. Subtracting 182, which is exactly 26 weeks, leaves 1 day. This confirms that we have advanced one weekday from the reference date. Because the reference day is Tuesday, the target day must be Wednesday. Both methods align and strengthen confidence in the result.

Why Other Options Are Wrong:
Monday would represent a shift of minus one day or six days forward, which does not match a remainder of 1. Tuesday would require the remainder to be 0 or a multiple of 7, meaning the total day difference would have to be divisible by 7, which it is not. Thursday would represent a shift of two days forward, which would come from a remainder of 2. Only Wednesday corresponds correctly to a remainder of 1 day after Tuesday.

Common Pitfalls:
Common mistakes include miscounting the number of days in a month, forgetting to exclude the starting day appropriately or making arithmetic slips in the total sum. Some students also confuse whether to include both endpoints or only one. Here we count the days that pass between 14th March and 13th September, and the modulo 7 calculation handles the wrap around. Careful month by month counting prevents errors.

Final Answer:
Pranay birthday on 13th September of the same year will fall on Wednesday.