Question
Download Solution PDFWhat was the day of the week on 17th June, 1998?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven date: 17 June 1998.
| Year | Odd Days |
| 100 | 5 odd days |
| 200 | 3 odd days |
| 300 | 1 odd days |
| 400 | 0 odd days |
Now,
Till 1600 → 0 odd days
Till 1900 (300 years) → 1 odd day
From 1900 to 1997 (97 years)
| Leap Year | 2 Odd days |
| Ordinary Year |
1 Odd day |
Number of leap years between 1900 and 1997
= (1997 - 1900) / 4
= 97 / 4 = 24 (only consider the whole number part)
Number of ordinary years
= 97 - 24 = 73
Therefore, total odd days in 97 years
= (24 * 2) + (73 * 1)
= 48 + 73 = 121
In 97 Years, the odd day count is 121.
So far, odd days until 1997 = 0 (for 1600 years) + 1 (for 300 years) + 121 = 122.
122 modulo 7 = 3 odd days (since 122 / 7 gives a remainder of 3).
From 1st January 1998 to 17th June 1998:
31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 17 (Jun) = 168 days.
Total odd days in 168 days = 168 / 7 = 24 weeks and 0 odd days.
Total odd days = 3 (odd days up to 1997) + 0 = 3 odd days.
⇒ 3 represents Wednesday.
So, 17 June 1998 is a Wednesday.
Hence, the correct answer is “Wednesday”.
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