Priya has her birthday on Tuesday, 11th April. In the same calendar year Rani was born on 31st August. On which day of the week does the birthday of Rani fall in that year?

Introduction / Context:
This problem is a calendar based reasoning question. You are told the day of the week for one date in a year and must determine the day of the week for another date in the same year. Such questions test your ability to count days across months, taking account of month lengths, and then convert the total day difference into a weekday shift using multiples of seven.

Given Data / Assumptions:

• Priya's birthday is on Tuesday, 11th April.
• Rani's birthday is on 31st August of the same year.
• We assume the usual Gregorian calendar with April having 30 days, June having 30 days and so on.
• The year may be leap or non leap, but both dates are after February, so the number of days between 11th April and 31st August is the same in both cases.

Concept / Approach:
The day of the week repeats every seven days, so we only care about the remainder when the number of days between the two dates is divided by 7. We count the days from 11th April to 31st August, convert this difference into an offset modulo 7 and then move forward that many days from Tuesday to get the day of the week for 31st August.

Step-by-Step Solution:
Step 1: Count the remaining days in April after 11th April. April has 30 days, so there are 30 - 11 = 19 days from 12th April to 30th April inclusive.Step 2: Count the days in May: 31 days.Step 3: Count the days in June: 30 days.Step 4: Count the days in July: 31 days.Step 5: Count the days in August from 1st to 31st: that gives 31 days.Step 6: Total days between 11th April and 31st August = 19 + 31 + 30 + 31 + 31.Step 7: Compute 19 + 31 = 50, 50 + 30 = 80, 80 + 31 = 111, 111 + 31 = 142 days.Step 8: Find 142 modulo 7. Since 7 * 20 = 140, 142 - 140 = 2, so the remainder is 2.Step 9: A difference of 142 days corresponds to moving 2 days forward in the week cycle.Step 10: Starting from Tuesday, move forward 2 days: Wednesday is one day later, Thursday is two days later.

Verification / Alternative check:
You can perform a quick mental check by grouping days in multiples of seven. For example, 7 days after Tuesday is again Tuesday, 14 days after is Tuesday and so on. After 140 days, which is a multiple of 7, you land again on Tuesday. Two more days then move you to Thursday. This confirms that we have correctly used the concept of modulo 7 and that the computed weekday is consistent with the day cycle.

Why Other Options Are Wrong:
Monday or Tuesday would correspond to a shift of 6 or 0 days, which does not match a remainder of 2 when 142 is divided by 7.Wednesday corresponds to a shift of 1 day from Tuesday, but the remainder is 2.Friday would correspond to a shift of 3 days from Tuesday, which again contradicts the calculated shift of 2 days.

Common Pitfalls:
Sometimes students mistakenly include or exclude one of the boundary dates incorrectly when counting days, leading to an off by one error. Others may use incorrect month lengths, especially for April, June and August. A safe approach is always to write down the months and their days, then carefully add them. Finally, always convert the total into a remainder modulo 7 before moving along the weekdays, instead of stepping through every single day mentally.

Final Answer:
Rani's birthday on 31st August in that year falls on Thursday.