Devansh's birthday in a certain year falls on Friday, 14th April. In the same year, Rohan was born on 20th September. On which day of the week does Rohan's birthday fall?

Introduction / Context:
This question again relates two dates within the same year and asks you to find the weekday for the second date, given the weekday for the first one. It tests your ability to count days through several months and to convert that count into a weekday shift using multiples of 7.

Given Data / Assumptions:

• Devansh's birthday is on Friday, 14th April in a certain year.
• Rohan's birthday is on 20th September in the same year.
• We must determine the day of the week for 20th September of that year.
• Both dates are after February, so any leap day in that year would affect both dates equally and does not change their difference.

Concept / Approach:
We calculate the total number of days between 14th April and 20th September and then reduce this total modulo 7 to find how many days ahead we must move from Friday. A remainder of 0 means the same weekday, a remainder of 1 means one day ahead, and so on, up to 6 days ahead.

Step-by-Step Solution:
Step 1: Determine days remaining in April after 14th April. April has 30 days, so from 15th April to 30th April = 16 days. Step 2: Count the days in full months from May to August: May 31, June 30, July 31, August 31. Step 3: Sum of days from May to August = 31 + 30 + 31 + 31 = 123 days. Step 4: Count days in September from 1st to 20th September = 20 days. Step 5: Total days from 14th April to 20th September = 16 (April) + 123 (May–August) + 20 (September) = 159 days. Step 6: Compute 159 mod 7. We know 7 * 22 = 154, leaving a remainder of 5. Step 7: A remainder of 5 means we move 5 days forward from Friday. Step 8: Counting forward: Friday → Saturday (1), Sunday (2), Monday (3), Tuesday (4), Wednesday (5). Step 9: Therefore, Rohan's birthday on 20th September falls on a Wednesday.

Verification / Alternative check:
You can verify by cross-checking with a known calendar for a concrete year where 14th April falls on a Friday and examining the weekday on 20th September in that same year. A correct modern example confirms that the computed weekday is Wednesday. Because the relative difference in days is fixed, any year with 14th April as a Friday will place 20th September on a Wednesday.

Why Other Options Are Wrong:
Tuesday: This is only 4 days ahead of Friday and would correspond to a remainder of 4 mod 7, but our calculation gives a remainder of 5.

Thursday: This is 6 days ahead of Friday, corresponding to a remainder of 6, which does not match the total day difference.

Friday: This suggests no effective shift (remainder 0), but the difference of 159 days is not a multiple of 7.

Monday: This is 3 days ahead of Friday, which would require a remainder of 3, not supported by our calculation.

Common Pitfalls:
Errors often occur in counting the days left in April or in adding up the days across multiple months. Another frequent mistake is failing to reduce the total number of days correctly using modulo 7, which leads to an incorrect weekday shift. Carefully writing each month's contribution and performing the modulo calculation separately helps maintain accuracy.

Final Answer:
Rohan's birthday on 20th September falls on a Wednesday.