In a certain year, Aarav has his birthday on Sunday, 12 March. In the same year, Madhup was born on 10 August. On which day of the week does 10 August fall in that year?

Introduction / Context:
This is a classic calendar problem where you use the known weekday for one date to determine the weekday for another date in the same year. Aarav has a birthday on Sunday, 12 March, and we are asked to find the weekday for 10 August in that same year. The challenge is to count the number of days between the two dates and then adjust the weekday accordingly using the modulo 7 concept.

Given Data / Assumptions:

• Aarav birthday is on 12 March, and that day is Sunday.
• Madhup birthday is on 10 August in the same year.
• We assume the usual Gregorian calendar month lengths: March 31 days, April 30, May 31, June 30, July 31, and August 31.
• The year type (leap or non leap) does not affect the difference between these two dates because both lie after February.

Concept / Approach:
To determine the weekday on 10 August, we need to count how many days lie between 12 March and 10 August. Then we divide this number by 7 to get the remainder, which tells us how many steps to move forward from Sunday. Because weekdays cycle every 7 days, only the remainder modulo 7 changes the weekday; full multiples of 7 do not affect the day of the week.

Step-by-Step Solution:
Step 1: Count days from 13 March to the end of March. There are 31 − 12 = 19 days remaining in March after 12 March. Step 2: April has 30 days, May has 31 days, June has 30 days, and July has 31 days. Step 3: From 1 April to 31 July, total days are 30 + 31 + 30 + 31 = 122 days. Step 4: From 1 August to 10 August inclusive there are 10 days. Step 5: The total number of days from 13 March up to and including 10 August is 19 + 122 + 10 = 151 days. Step 6: To move from 12 March to 10 August, we advance 151 days. Compute 151 mod 7, which is 4. Step 7: A remainder of 4 means we move four weekdays forward from Sunday: Monday, Tuesday, Wednesday, Thursday. Therefore, 10 August falls on Thursday.

Verification / Alternative check:
You can also regroup the 151 days into blocks of 7 days to simplify mental calculation. Because 147 is divisible by 7, we can view 151 as 147 + 4. The 147 days correspond to exactly 21 weeks, which do not change the weekday at all, and only the remaining 4 days matter. Starting from Sunday and moving four steps forward again yields Thursday. If you loosely sketch a mini calendar from mid March to mid August and mark every seventh day, you will also see the alignment landing on Thursday for 10 August.

Why Other Options Are Wrong:
Wednesday corresponds to shifting only three days forward from Sunday, which does not match the remainder of four days that we obtained. Friday would require a shift of five days, and Saturday would require a shift of six days, neither of which equals the remainder of 4. Only Thursday aligns with the four day forward shift indicated by 151 mod 7.

Common Pitfalls:
Common errors include miscounting the days in the months between March and August or forgetting whether the count should be inclusive or exclusive of the starting date. Another mistake is to treat both dates as if they were at month boundaries, which can lead to small off by one errors. Ensure that you correctly handle the leftover days in both the starting month and the ending month, and always reduce the total by modulo 7 before adjusting the weekday.

Final Answer:
Therefore, Madhup birthday on 10 August falls on a Thursday in that year.