Introduction / Context:
This is another example of finding the weekday for a future date within the same year. The reference date and its weekday are known, and the task is to translate the time gap into a weekday shift. This kind of problem builds fluency with months, total day counts and the repeating seven day pattern, all of which are very useful in calendar based aptitude questions.
Given Data / Assumptions:
- The birthday of Hansh is on Monday 5 June in a certain year.
- The birthday of Tushar is on 11 December in the same year.
- We must determine the weekday for 11 December.
- Leap year status does not matter because both dates are well after February.
Concept / Approach:We compute the number of days between 5 June and 11 December and then find the remainder when this number is divided by 7. Every complete block of 7 days forms a full week and does not change the weekday. Only the remainder, called the odd days, changes the weekday when counted forward from the starting day, which is Monday.
Step-by-Step Solution:Step 1: Determine remaining days in June after 5 June. Since June has 30 days, remaining days are 30 - 5 = 25.Step 2: Add full months from July to November. July has 31 days, August 31, September 30, October 31 and November 30. Total days in these months equal 31 + 31 + 30 + 31 + 30 = 153.Step 3: Add days in December up to 11 December, which gives 11 days.Step 4: Total days between the birthdays equals 25 + 153 + 11 = 189 days.Step 5: Compute 189 modulo 7. Since 7 * 27 = 189 exactly, the remainder is 0. This means there are no odd days between the dates and the weekday remains unchanged. Therefore Tushar's birthday falls on Monday.Verification / Alternative check:Interpreting 189 as 27 weeks provides an intuitive check. Every full week consists of 7 days and brings the calendar back to the same weekday. So after 27 weeks the weekday must be the same as on the starting date. This confirms that no shift in weekday occurs and validates our result.
Why Other Options Are Wrong:Sunday would represent a one day shift backward from Monday, which would require a remainder of 6 or 1 odd day instead of 0.Wednesday corresponds to a two day shift from Monday, which conflicts with the calculation that shows zero odd days.Tuesday is three days ahead of Saturday or one day ahead of Monday, again not supported by the remainder of 0.Common Pitfalls:Candidates sometimes believe that when dates are far apart the weekday must change. However, as this example shows, if the total difference is a multiple of 7, the weekday does not change. Another mistake is incorrect counting of days in the months, especially for June, September and November which have 30 days. Careful listing of month lengths helps avoid such errors.
Final Answer:Tushar's birthday on 11 December falls on Monday.
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