What was the day on 31st Oct 1984?
Explanation:
Here we need to break days till 31st Oct 1984.
Complete years = 1983
Odd days in first 1600 years = 0 Odd days in next 300 years = 1 Odd days in next 83 years (20 leap and 63 non-leap years) = 20 × 2 + 63 × 1 = 103.
∴ Odd days in complete years = 0 + 1 + 103 = 104 odd days.
∴ Odd days in complete years = Remainder (104 ÷ 7) = 6 odd days.
Incomplete year (1984, a leap year)
Jan + Feb + Mar = 0 odd days, Apr + May + Jun = 0 = odd days, Jul + Aug + Sep = 1 odd day Oct = 31
∴ Odd days in incomplete year = 0 + 0 + 1 + 31 = 32 odd days = 4 odd days.
∴ Total odd days till 31st Oct 1984 = 6 + 4 = 10 odd days = 3 odd days.
∴ Day of the week on 31st Oct 1984 will be 3 days after Sunday i.e., Wednesday.
Hence, option (d).
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