Advik celebrates his birthday on Monday 19 June in a certain year. In the same year Nishith celebrates his birthday on 17 November. On which day of the week does Nishith's birthday fall?

Difficulty: Medium

Correct Answer: Friday

Explanation:


Introduction / Context:
This question continues the theme of weekday calculations within a single year. We know the weekday for one date and must find the weekday for another date in the same year. The problem exercises the ability to count days correctly across several months and then convert that difference into an effective weekday shift using the idea of odd days.

Given Data / Assumptions:

  • Advik has his birthday on Monday 19 June in a particular year.
  • Nishith has his birthday on 17 November in the same year.
  • We want the day of the week for 17 November.
  • Leap year status does not influence the answer because all the counting is done after February.

Concept / Approach:
We first compute the number of days between the two dates. Then we divide that number by 7 to find the remainder, which gives the number of odd days. Each group of 7 days is a complete week and does not affect the weekday. Only the remainder shifts the weekday forward from the starting day, Monday, to the final weekday for Nishith's birthday.

Step-by-Step Solution:
Step 1: Determine remaining days in June after 19 June. June has 30 days, so remaining days are 30 - 19 = 11.Step 2: Add days in the full months from July to October. July has 31 days, August 31, September 30 and October 31. Total days in these months equal 31 + 31 + 30 + 31 = 123.Step 3: Add days in November up to 17 November, which gives 17 days.Step 4: Total days between 19 June and 17 November equal 11 + 123 + 17 = 151.Step 5: Compute 151 modulo 7. Since 7 * 21 = 147, the remainder is 4. Therefore there are 4 odd days between the two birthdays. Starting from Monday and moving forward 4 days gives Tuesday (1), Wednesday (2), Thursday (3) and Friday (4). Hence Nishith's birthday falls on Friday.
Verification / Alternative check:
We can also interpret 151 as 147 plus 4. Since 147 is exactly 21 weeks, it leads back to the same weekday, leaving a net effect of 4 extra days. When these 4 days are counted forward from Monday, the weekday lands on Friday. This alternative view reinforces the earlier calculation and confirms the result.

Why Other Options Are Wrong:
Saturday would require a shift of 5 days from Monday, which is not supported by the remainder of 4.Wednesday corresponds to a shift of 2 days from Monday, which does not match the calculated shift.Sunday would represent either a single step backward from Monday or 6 steps forward, neither of which agrees with the 4 odd days.
Common Pitfalls:
Many students miscalculate the number of days in one of the months or accidentally include 19 June itself when counting. Others misinterpret the remainder when dividing by 7 and move in the wrong direction on the weekday cycle. A clear month wise breakdown and conscious forward counting from the starting weekday help avoid these traps.

Final Answer:
Nishith's birthday on 17 November falls on Friday.

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